bluuebunny/crossref_metadata_2025 huggingface dataset:
Spectral Estimates for Towers of Noncompact Quotients
Authors: Deitmar Anton , Hoffman Werner
Published: December 2010

We prove a uniform upper estimate on the number of cuspidal eigenvalues of the Γ-automorphic Laplacian below a given bound when Γ varies in a family of congruence subgroups of a given reductive linear algebraic group. Each Γ in the family is assumed to contain a principal congruence subgroup whose index in Γ does not exceed a fixed number. The bound we prove depends linearly on the covolume of Γ and is deduced from the analogous result about the cut-off Laplacian. The proof generalizes the heat-kernel method which has been applied by Donnelly in the case of a fixed lattice Γ.
A Homotopy of Quiver Morphisms with Applications to Representations
Authors: Enochs Edgar E. , Herzog Ivo
Published: December 2010

It is shown that a morphism of quivers having a certain path lifting property has a decomposition that mimics the decomposition of maps of topological spaces into homotopy equivalences composed with fibrations. Such a decomposition enables one to describe the right adjoint of the restriction of the representation functor along a morphism of quivers having this path lifting property. These right adjoint functors are used to construct injective representations of quivers. As an application, the injective representations of the cyclic quivers are classified when the base ring is left noetherian. In particular, the indecomposable injective representations are described in terms of the injective indecomposable R-modules and the injective indecomposable R[x; x−1]-modules.
Exterior Univalent Harmonic Mappings With Finite Blaschke Dilatations
Authors: Bshouty D. , Hengartner W.
Published: December 2010

In this article we characterize the univalent harmonic mappings from the exterior of the unit disk, Δ, onto a simply connected domain Ω containing infinity and which are solutions of the system of elliptic partial differential equations where the second dilatation function a(z) is a finite Blaschke product. At the end of this article, we apply our results to nonparametric minimal surfaces having the property that the image of its Gauss map is the upper half-sphere covered once or twice.
Smooth Finite Dimensional Embeddings
Authors: Mansfield R. , Movahedi-Lankarani H. , Wells R.
Published: December 2010

We give necessary and sufficient conditions for a norm-compact subset of a Hilbert space to admit aC1embedding into a finite dimensional Euclidean space. Using quasibundles, we prove a structure theorem saying that the stratum ofn-dimensional points is contained in ann-dimensionalC1submanifold of the ambient Hilbert space. This work sharpens and extends earlier results of G. Glaeser on paratingents. As byproducts we obtain smoothing theorems for compact subsets of Hilbert space and disjunction theorems for locally compact subsets of Euclidean space.
On Functions Satisfying Modular Equations for Infinitely Many Primes
Authors: Kozlov Dmitry N.
Published: December 2010

In this paper we study properties of the functions which satisfy modular equations for infinitely many primes. The two main results are:

1)

every such function is analytic in the upper half plane;

2)

if such function takes the same value in two different pointsz1andz2then there exists anf-preserving analytic bijection between neighbourhoods ofz1andz2.
The Homology of Abelian Covers of Knotted Graphs
Authors: Litherland R. A.
Published: December 2010

Let be a regular branched cover of a homology 3-sphere M with deck group and branch set a trivalent graph Γ; such a cover is determined by a coloring of the edges of Γ with elements of G. For each index-2 subgroup H of G, MH = /H is a double branched cover of M. Sakuma has proved that H1() is isomorphic, modulo 2-torsion, to ⊕HH1(MH), and has shown that H1() is determined up to isomorphism by ⊕HH1(MH) in certain cases; specifically, when d = 2 and the coloring is such that the branch set of each cover MH → M is connected, and when d = 3 and Γ is the complete graph K4. We prove this for a larger class of coverings: when d = 2, for any coloring of a connected graph; when d = 3 or 4, for an infinite class of colored graphs; and when d = 5, for a single coloring of the Petersen graph.
Endoscopic L-Functions and a Combinatorial Identity
Authors: Arthur James
Published: December 2010

The trace formula contains terms on the spectral side that are constructed from unramified automorphic L-functions. We shall establish an identify that relates these terms with corresponding terms attached to endoscopic groups of G. In the process, we shall show that the L-functions of G that come from automorphic representations of endoscopic groups have meromorphic continuation.
Reflection Subquotients of Unitary Reflection Groups
Authors: Lehrer G. I. , Springer T. A.
Published: December 2010

Let G be a finite group generated by (pseudo-) reflections in a complex vector space and let g be any linear transformation which normalises G. In an earlier paper, the authors showed how to associate with any maximal eigenspace of an element of the coset gG, a subquotient of G which acts as a reflection group on the eigenspace. In this work, we address the questions of irreducibility and the coexponents of this subquotient, as well as centralisers in G of certain elements of the coset. A criterion is also given in terms of the invariant degrees of G for an integer to be regular for G. A key tool is the investigation of extensions of invariant vector fields on the eigenspace, which leads to some results and questions concerning the geometry of intersections of invariant hypersurfaces.
Comparison of K-Theory Galois Module Structure Invariants
Authors: Chinburg T. , Kolster M. , Snaith V. P.
Published: December 2010

We prove that two, apparently different, class-group valued Galoismodule structure invariants associated to the algebraic K-groups of rings of algebraic integers coincide. This comparison result is particularly important in making explicit calculations.
Numerical Ranges Arising from Simple Lie Algebras
Authors: Li Chi-Kwong , Tam Tin-Yau
Published: December 2010

A unified formulation is given to various generalizations of the classical numerical range including the c-numerical range, congruence numerical range, q-numerical range and von Neumann range. Attention is given to those cases having connections with classical simple real Lie algebras. Convexity and inclusion relation involving those generalized numerical ranges are investigated. The underlying geometry is emphasized.
On Orbit Closures of Symmetric Subgroups in Flag Varieties
Authors: Brion Michel , Helminck Aloysius G.
Published: December 2010

We study K-orbits in G/P where G is a complex connected reductive group, P ⊆ G is a parabolic subgroup, and K ⊆ G is the fixed point subgroup of an involutive automorphism θ. Generalizing work of Springer, we parametrize the (finite) orbit set K \ G/P and we determine the isotropy groups. As a consequence, we describe the closed (resp. affine) orbits in terms of θ-stable (resp. θ-split) parabolic subgroups. We also describe the decomposition of any (K, P)-double coset in G into (K, B)-double cosets, where B ⊆ P is a Borel subgroup. Finally, for certain K-orbit closures X ⊆ G/B, and for any homogeneous line bundle on G/B having nonzero global sections, we show that the restriction map resX : H0(G/B, ) → H0(X, ) is surjective and that Hi(X, ) = 0 for i ≥ 1. Moreover, we describe the K-module H0(X, ). This gives information on the restriction to K of the simple G-module H0(G/B, ). Our construction is a geometric analogue of Vogan and Sepanski’s approach to extremal K-types.
Singularités quasi-ordinaires toriques et polyèdre de Newton du discriminant
Authors: González Pérez P. D.
Published: December 2010

Nous étudions les polynômes à coefficients dans l’anneau de germes de fonctions holomorphes au point spécial d’une variété torique affine. Nous généralisons à ce cas la paramétrisation classique des singularités quasi-ordinaires. Cela fait intervenir d’une part une généralization de l’algorithme de Newton-Puiseux, et d’autre part une relation entre le polyèdre de Newton du discriminant de F par rapport à Y et celui de F au moyen du polytope-fibre de Billera et Sturmfels [3]. Cela nous permet enfin de calculer, sous des hypothèses de non dégénérescence, les sommets du polyèdre de Newton du discriminant a partir de celui de F, et les coefficients correspondants à partir des coefficients des exposants de F qui sont dans les arˆetes de son polyèdre de Newton.
An Intertwining Result for p-adic Groups
Authors: Adler Jeffrey D. , Roche Alan
Published: December 2010

For a reductive p-adic group G, we compute the supports of the Hecke algebras for the K-types for G lying in a certain frequently-occurring class. When G is classical, we compute the intertwining between any two such K-types.
Correspondences, von Neumann Algebras and Holomorphic L2 Torsion
Authors: Carey A. , Farber M. , Mathai V.
Published: December 2010

Given a holomorphic Hilbertian bundle on a compact complex manifold, we introduce the notion of holomorphic L2 torsion, which lies in the determinant line of the twisted L2 Dolbeault cohomology and represents a volume element there. Here we utilise the theory of determinant lines of Hilbertian modules over finite von Neumann algebras as developed in [CFM]. This specialises to the Ray-Singer-Quillen holomorphic torsion in the finite dimensional case. We compute ametric variation formula for the holomorphic L2 torsion, which shows that it is not in general independent of the choice of Hermitian metrics on the complex manifold and on the holomorphic Hilbertian bundle, which are needed to define it. We therefore initiate the theory of correspondences of determinant lines, that enables us to define a relative holomorphic L2 torsion for a pair of flat Hilbertian bundles, which we prove is independent of the choice of Hermitian metrics on the complex manifold and on the flat Hilbertian bundles.
An Automorphic Theta Module for Quaternionic Exceptional Groups
Authors: Gan Wee Teck
Published: December 2010

We construct an automorphic realization of the global minimal representation of quaternionic exceptional groups, using the theory of Eisenstein series, and use this for the study of theta correspondences.
The Distributions in the Invariant Trace Formula Are Supported on Characters
Authors: Kottwitz Robert E. , Rogawski Jonathan D.
Published: December 2010

J. Arthur put the trace formula in invariant form for all connected reductive groups and certain disconnected ones. However his work was written so as to apply to the general disconnected case, modulo two missing ingredients. This paper supplies one of those missing ingredients, namely an argument in Galois cohomology of a kind first used by D. Kazhdan in the connected case.
W-Groups under Quadratic Extensions of Fields
Authors: Mináč Ján , Smith Tara L.
Published: December 2010

To each field F of characteristic not 2, one can associate a certain Galois group , the so-called W-group of F, which carries essentially the same information as the Witt ring W(F) of F. In this paperwe investigate the connection between and (√a), where F(√a) is a proper quadratic extension of F. We obtain a precise description in the case when F is a pythagorean formally real field and a = −1, and show that the W-group of a proper field extension K/F is a subgroup of the W-group of F if and only if F is a formally real pythagorean field and K = F(√−1). This theorem can be viewed as an analogue of the classical Artin-Schreier’s theorem describing fields fixed by finite subgroups of absolute Galois groups. We also obtain precise results in the case when a is a double-rigid element in F. Some of these results carry over to the general setting.
Real Interpolation with Logarithmic Functors and Reiteration
Authors: Evans W. D. , Opic B.
Published: December 2010

We present “reiteration theorems” with limiting values θ = 0 and θ = 1 for a real interpolation method involving broken-logarithmic functors. The resulting spaces lie outside of the original scale of spaces and to describe them new interpolation functors are introduced. For an ordered couple of (quasi-) Banach spaces similar results were presented without proofs by Doktorskii in [D].
Canonical Resolution of a Quasi-ordinary Surface Singularity
Authors: Ban Chunsheng , McEwan Lee J.
Published: December 2010

We describe the embedded resolution of an irreducible quasi-ordinary surface singularity (V, p) which results from applying the canonical resolution of Bierstone-Milman to (V, p). We show that this process depends solely on the characteristic pairs of (V, p), as predicted by Lipman. We describe the process explicitly enough that a resolution graph for f could in principle be obtained by computer using only the characteristic pairs.
Orbital Integrals on p-Adic Lie Algebras
Authors: Herb Rebecca A.
Published: December 2010

Let G be a connected reductive p-adic group and let be its Lie algebra. Let be any G-orbit in . Then the orbital integral corresponding to is an invariant distribution on , and Harish-Chandra proved that its Fourier transform is a locally constant function on the set of regular semisimple elements of . If is a Cartan subalgebra of , and ω is a compact subset of ∩ , we give a formula for (tH) for H ε ω and t ε F× sufficiently large. In the case that is a regular semisimple orbit, the formula is already known by work of Waldspurger. In the case that is a nilpotent orbit, the behavior of at infinity is already known because of its homogeneity properties. The general case combines aspects of these two extreme cases. The formula for at infinity can be used to formulate a “theory of the constant term” for the space of distributions spanned by the Fourier transforms of orbital integrals. It can also be used to show that the Fourier transforms of orbital integrals are “linearly independent at infinity.”
Stratification Theory from the Weighted Point of View
Authors: Fukui Toshizumi , Paunescu Laurentiu
Published: December 2010

In this paper, we investigate stratification theory in terms of the defining equations of strata and maps (without tube systems), offering a concrete approach to show that some given family is topologically trivial. In this approach, we consider a weighted version of (w)-regularity condition and Kuo’s ratio test condition.
Group Actions and Codes
Authors: Puppe V.
Published: December 2010

A 2-action with “maximal number of isolated fixed points” (i.e., with only isolated fixed points such that dimk(⊕iHi (M; k)) = |M2|, k = ) on a 3-dimensional, closed manifold determines a binary self-dual code of length = . In turn this code determines the cohomology algebra H*(M; k) and the equivariant cohomology . Hence, from results on binary self-dual codes one gets information about the cohomology type of 3-manifolds which admit involutions with maximal number of isolated fixed points. In particular, “most” cohomology types of closed 3-manifolds do not admit such involutions. Generalizations of the above result are possible in several directions, e.g., one gets that “most” cohomology types (over ) of closed 3-manifolds do not admit a non-trivial involution.
Nombres premiers de la forme ⌊nc⌋
Authors: Rivat Joël , Sargos Patrick
Published: December 2010

For c > 1 we denote by πc(x) the number of integers n ≤ x such that ⌊nc⌋ is prime. In 1953, Piatetski-Shapiro has proved thatholds for c < 12/11. Many authors have extended this range, which measures our progress in exponential sums techniques. In this article we obtain c < 1.16117….
Descending Rational Points on Elliptic Curves to Smaller Fields
Authors: Akbary Amir , Kumar Murty V.
Published: December 2010

In this paper, we study the Mordell-Weil group of an elliptic curve as a Galois module. We consider an elliptic curve E defined over a number field K whose Mordell-Weil rank over a Galois extension F is 1, 2 or 3. We show that E acquires a point (points) of infinite order over a field whose Galois group is one of Cn×Cm (n = 1, 2, 3, 4, 6, m = 1, 2), Dn×Cm (n = 2, 3, 4, 6, m = 1, 2), A4×Cm (m = 1, 2), S4 × Cm (m = 1, 2). Next, we consider the case where E has complex multiplication by the ring of integers of an imaginary quadratic field contained in K. Suppose that the -rank over a Galois extension F is 1 or 2. If ≠ and and h (class number of ) is odd, we show that E acquires positive -rank over a cyclic extension of K or over a field whose Galois group is one of SL2(/3), an extension of SL2(/3) by /2, or a central extension by the dihedral group. Finally, we discuss the relation of the above results to the vanishing of L-functions.
Ideal Structure of Multiplier Algebras of Simple C*-algebras With Real Rank Zero
Authors: Perera Francesc
Published: December 2010

We give a description of the monoid of Murray-von Neumann equivalence classes of projections for multiplier algebras of a wide class of σ-unital simple C*-algebras A with real rank zero and stable rank one. The lattice of ideals of this monoid, which is known to be crucial for understanding the ideal structure of themultiplier algebra , is therefore analyzed. In important cases it is shown that, if A has finite scale then the quotient of modulo any closed ideal I that properly contains A has stable rank one. The intricacy of the ideal structure of is reflected in the fact that can have uncountably many different quotients, each one having uncountably many closed ideals forming a chain with respect to inclusion.
Seiberg-Witten Invariants of Lens Spaces
Authors: Nicolaescu Liviu I.
Published: December 2010

We show that the Seiberg-Witten invariants of a lens space determine and are determined by its Casson-Walker invariant and its Reidemeister-Turaev torsion.
Zeta Functions and ‘Kontsevich Invariants’ on Singular Varieties
Authors: Veys Willem
Published: December 2010

Let X be a nonsingular algebraic variety in characteristic zero. To an effective divisor on X Kontsevich has associated a certain motivic integral, living in a completion of the Grothendieck ring of algebraic varieties. He used this invariant to show that birational (smooth, projective) Calabi-Yau varieties have the same Hodge numbers. Then Denef and Loeser introduced the invariant motivic (Igusa) zeta function, associated to a regular function on X, which specializes to both the classical p-adic Igusa zeta function and the topological zeta function, and also to Kontsevich's invariant.

This paper treats a generalization to singular varieties. Batyrev already considered such a ‘Kontsevich invariant’ for log terminal varieties (on the level of Hodge polynomials of varieties instead of in the Grothendieck ring), and previously we introduced a motivic zeta function on normal surface germs. Here on any ℚ-Gorenstein variety X we associate a motivic zeta function and a ‘Kontsevich invariant’ to effective ℚ-Cartier divisors on X whose support contains the singular locus of X.
Ranks of Algebras of ContinuousC*-Algebra Valued Functions
Authors: Nagisa Masaru , Osaka Hiroyuki , Phillips N. Christopher
Published: December 2010

We prove a number of results about the stable and particularly the real ranks of tensor products ofC*-algebras under the assumption that one of the factors is commutative. In particular, we prove the following:

(1)

IfXis any locally compact σ-compact Hausdorff space andAis anyC*-algebra, then RR(C0(X) ⊗A) ≤ dim(X) + RR(A).

(2)

IfXis any locally compact Hausdorff space andAis any purely infinite simpleC*-algebra, then RR(C0(X) ⊗A) ≤ 1.

(3)

RR(C([0, 1]) ⊗A) ≥ 1 for any nonzeroC*-algebraA, and sr(C([0, 1]2) ⊗A) ≥ 2 for any unitalC*-algebraA.

(4)

IfAis a unitalC*-algebra such that RR(A) = 0, sr(A) = 1, andK1(A) = 0, then sr(C([0, 1]) ⊗A) = 1.

(5)

There is a simple separable unital nuclearC*-algebraAsuch that RR(A) = 1 and sr(C([0, 1]) ⊗A) = 1.
The Donaldson-Hitchin-Kobayashi Correspondence for Parabolic Bundles over Orbifold Surfaces
Authors: Steer Brian , Wren Andrew
Published: December 2010

A theorem of Donaldson on the existence of Hermitian-Einstein metrics on stable holomorphic bundles over a compact Kähler surface is extended to bundles which are parabolic along an effective divisor with normal crossings. Orbifold methods, together with a suitable approximation theorem, are used following an approach successful for the case of Riemann surfaces.
Elementary Symmetric Polynomials in Numbers of Modulus 1
Authors: Cartwright Donald I. , Steger Tim
Published: December 2010

We describe the set of numbersσk(z1,…,zn+1), wherez1,…,zn+1are complex numbers of modulus 1 for whichz1z2…zn+1= 1, andσkdenotes thek-th elementary symmetric polynomial. Consequently, we give sharp constraints on the coefficients of a complex polynomial all of whose roots are of the same modulus. Another application is the calculation of the spectrum of certain adjacency operators arising naturally on a building of typeÃn.
Perverse Sheaves on Grassmannians
Authors: Braden Tom
Published: December 2010

We compute the category of perverse sheaves on Hermitian symmetric spaces in types A and D, constructible with respect to the Schubert stratification. The calculation is microlocal, and uses the action of the Borel group to study the geometry of the conormal variety Λ.
Approximations fortes pour des processus bivariés
Authors: Castelle Nathalie
Published: December 2010

Nous établissons un résultat d’approximation forte pour des processus bivariés ayant une partie gaussienne et une partie empirique. Ce résultat apporte un nouveau point de vue sur deux théorèmes hongrois bidimensionnels établis précédemment, concernant l’approximation par un processus de Kiefer d’un processus empirique uniforme unidimensionnel et l’approximation par un pont brownien bidimensionnel d’un processus empirique uniforme bidimensionnel. Nous les enrichissons un peu et montrons que sous leur nouvelle forme ils ne sont que deux énoncés d’un même résultat.
Local L-Functions for Split Spinor Groups
Authors: Asgari Mahdi
Published: December 2010

We study the local L-functions for Levi subgroups in split spinor groups defined via the Langlands-Shahidi method and prove a conjecture on their holomorphy in a half plane. These results have been used in the work of Kim and Shahidi on the functorial product for GL2 × GL3.
Cuntz Algebra States Defined by Implementers of Endomorphisms of the CAR Algebra
Authors: Gabriel Michael J.
Published: December 2010

We investigate representations of the Cuntz algebraon antisymmetric Fock spaceFa(𝒦1) defined by isometric implementers of certain quasi-free endomorphisms of the CAR algebra in pure quasi-free states φP1. We pay special attention to the vector states oncorresponding to these representations and the Fock vacuum, for which we obtain explicit formulae. Restricting these states to the gauge-invariant subalgebra, we find that for natural choices of implementers, they are again pure quasi-free and are, in fact, essentially the states φP1. We proceed to consider the case for an arbitrary pair of implementers, and deduce that these Cuntz algebra representations are irreducible, as are their restrictions to.

The endomorphisms ofB(Fa(𝒦)) associated with these representations ofare also considered.
Structure Theory of Totally Disconnected Locally Compact Groups via Graphs and Permutations
Authors: Möller Rögnvaldur G.
Published: December 2010

Willis's structure theory of totally disconnected locally compact groups is investigated in the context of permutation actions. This leads to new interpretations of the basic concepts in the theory and also to new proofs of the fundamental theorems and to several new results. The treatment of Willis's theory is self-contained and full proofs are given of all the fundamental results.
Octahedral Galois Representations Arising From Q-Curves of Degree 2
Authors: Fernández J. , Lario J-C. , Rio A.
Published: December 2010

Generically, one can attach to a Q-curve C octahedral representations ρ: Gal() → GL2() coming from the Galois action on the 3-torsion of those abelian varieties of GL2-type whose building block is C. When C is defined over a quadratic field and has an isogeny of degree 2 to its Galois conjugate, there exist such representations ρ having image into GL2(F9). Going the other way, we can ask which mod 3 octahedral representations ρ of Gal() arise from Q-curves in the above sense. We characterize those arising from quadratic Q-curves of degree 2. The approach makes use of Galois embedding techniques in GL2(F9), and the characterization can be given in terms of a quartic polynomial defining the S4-extension of Q corresponding to the projective representation .
Effective Actions of the Unitary Group on Complex Manifolds
Authors: Isaev A. V. , Kruzhilin N. G.
Published: December 2010

We classify all connected n-dimensional complex manifolds admitting effective actions of the unitary group Un by biholomorphic transformations. One consequence of this classification is a characterization of by its automorphism group.
The Continuous Hochschild Cochain Complex of a Scheme
Authors: Yekutieli Amnon
Published: December 2010

Let X be a separated finite type scheme over a noetherian base ring . There is a complex of topological -modules, called the complete Hochschild chain complex of X. To any -module —not necessarily quasi-coherent—we assign the complex of continuous Hochschild cochains with values in . Our first main result is that when X is smooth over there is a functorial isomorphism

in the derived category , where .

The second main result is that if X is smooth of relative dimension n and n! is invertible in K, then the standard maps induce a quasi-isomorphism

When this is the quasi-isomorphism underlying the Kontsevich Formality Theorem.

Combining the two results above we deduce a decomposition of the globalHochschild cohomology

where is the relative tangent sheaf.
Short Kloosterman Sums for Polynomials over Finite Fields
Authors: Banks William D. , Harcharras Asma , Shparlinski Igor E.
Published: December 2010

We extend to the setting of polynomials over a finite field certain estimates for short Kloosterman sums originally due to Karatsuba. Our estimates are then used to establish some uniformity of distribution results in the ring [x]/M(x) for collections of polynomials either of the form f−1g−1 or of the form f−1g−1 + afg, where f and g are polynomials coprime to M and of very small degree relative to M, and a is an arbitrary polynomial. We also give estimates for short Kloosterman sums where the summation runs over products of two irreducible polynomials of small degree. It is likely that this result can be used to give an improvement of the Brun-Titchmarsh theorem for polynomials over finite fields.
Graph Subspaces and the Spectral Shift Function
Authors: Albeverio Sergio , Makarov Konstantin A. , Motovilov Alexander K.
Published: December 2010

We obtain a new representation for the solution to the operator Sylvester equation in the form of a Stieltjes operator integral. We also formulate new sufficient conditions for the strong solvability of the operator Riccati equation that ensures the existence of reducing graph subspaces for block operator matrices. Next, we extend the concept of the Lifshits-Krein spectral shift function associated with a pair of self-adjoint operators to the case of pairs of admissible operators that are similar to self-adjoint operators. Based on this new concept we express the spectral shift function arising in a perturbation problem for block operator matrices in terms of the angular operators associated with the corresponding perturbed and unperturbed eigenspaces.
Automorphismes modérés de l'espace affine
Authors: Edo Eric
Published: December 2010

Le problème de Jung-Nagata (cf. [J], [N]) consiste à savoir s'il existe des automorphismes dek[x; y; z] qui ne sont pas modérés. Nous proposons une approche nouvelle de cette question, fondée sur l'utilisation de la théorie des automates et du polygone de Newton. Cette approche permet notamment de généraliser de façon significative les résultats de [A].
Higher Dimensional Asymptotic Cycles
Authors: Schwartzman Sol
Published: December 2010

Given a p-dimensional oriented foliation of an n-dimensional compact manifold Mn and a transversal invariant measure τ, Sullivan has defined an element of Hp(Mn; R). This generalized the notion of a μ-asymptotic cycle, which was originally defined for actions of the real line on compact spaces preserving an invariant measure μ. In this one-dimensional case there was a natural 1—1 correspondence between transversal invariant measures τ and invariant measures μ when one had a smooth flow without stationary points.

For what we call an oriented action of a connected Lie group on a compact manifold we again get in this paper such a correspondence, provided we have what we call a positive quantifier. (In the one-dimensional case such a quantifier is provided by the vector field defining the flow.) Sufficient conditions for the existence of such a quantifier are given, together with some applications.
Surfaces with pg = q = 2 and an Irrational Pencil
Authors: Zucconi Francesco
Published: December 2010

We describe the irrational pencils on surfaces of general type with pg = q = 2.
A Note on Cyclotomic Euler Systems and the Double Complex Method
Authors: Anderson Greg W. , Ouyang Yi
Published: December 2010

Letbe a finite real abelian extension of ℚ. LetMbe an odd positive integer. For every squarefree positive integerrthe prime factors of which are congruent to 1 moduloMand split completely in, the corresponding Kolyvagin classsatisfies a remarkable and crucial recursion which for each prime number ℓ dividingrdetermines the order of vanishing of κrat each place ofabove ℓ in terms of κr/ℓ. In this note we give the recursion a new and universal interpretation with the help of the double complex method introduced by Anderson and further developed by Das and Ouyang. Namely, we show that the recursion satis_ed by Kolyvagin classes is the specialization of a universal recursion independent ofsatisfied by universal Kolyvagin classes in the group cohomology of the universal ordinary distributionà laKubert tensored with ℤ=Mℤ. Further, we show by a method involving a variant of the diagonal shift operation introduced by Das that certain group cohomology classes belonging (up to sign) to a basis previously constructed by Ouyang also satisfy the universal recursion.
Adic Topologies for the Rational Integers
Authors: Broughan Kevin A.
Published: December 2010

A topology on ℤ, which gives a nice proof that the set of prime integers is infinite, is characterised and examined. It is found to be homeomorphic to ℚ, with a compact completion homeomorphic to the Cantor set. It has a natural place in a family of topologies on ℤ, which includes the p-adics, and one in which the set of rational primes ℙ is dense. Examples from number theory are given, including the primes and squares, Fermat numbers, Fibonacci numbers and k-free numbers.
The Closure Ordering of Nilpotent Orbits of the Complex Symmetric Pair (SOp+q, SOp × SOq)
Authors: Ðoković Dragomir Ž. , Litvinov Michael
Published: December 2010

The main problem that is solved in this paper has the following simple formulation (which is not used in its solution). The group K = Op(C) × Oq(C) acts on the space Mp, q of p × q complex matrices by (a; b) · x = axb–1, and so does its identity component K0 = SOp(C)×SOq(C). A K-orbit (or K0-orbit) in Mp,q is said to be nilpotent if its closure contains the zero matrix. The closure, , of a nilpotent K-orbit (resp. K0-orbit) in Mp,q is a union of and some nilpotent K-orbits (resp. K0-orbits) of smaller dimensions. The description of the closure of nilpotent K-orbits has been known for some time, but not so for the nilpotent K0-orbits. A conjecture describing the closure of nilpotent K0-orbits was proposed in [11] and verièd when min(p, q) ≤ 7. In this paper we prove the conjecture. The proof is based on a study of two prehomogeneous vector spaces attached to and determination of the basic relative invariants of these spaces.

The above problem is equivalent to the problem of describing the closure of nilpotent orbits in the real Lie algebra so(p, q) under the adjoint action of the identity component of the real orthogonal group O(p, q).
On a Certain Residual Spectrum of Sp8
Authors: Pogge James Todd
Published: December 2010

Let G = Sp2n be the symplectic group defined over a number field F. Let 𝔸 be the ring of adeles. A fundamental problem in the theory of automorphic forms is to decompose the right regular representation of G(𝔸) acting on the Hilbert space L2 (G(F) \ G(𝔸)). Main contributions have been made by Langlands. He described, using his theory of Eisenstein series, an orthogonal decomposition of this space of the form: , where (M, π) is a Levi subgroup with a cuspidal automorphic representation π taken modulo conjugacy. (Here we normalize π so that the action of the maximal split torus in the center of G at the archimedean places is trivial.) and is a space of residues of Eisenstein series associated to (M, π). In this paper, we will completely determine the space , when M ≃ GL2 × GL2. This is the first result on the residual spectrum for non-maximal, non-Borel parabolic subgroups, other than GLn.
Spectral Properties of the Commutator of Bergman's Projection and the Operator of Multiplication by an Analytic Function
Authors: Dostanić Milutin R.
Published: December 2010

It is shown that the singular values of the operator aP–Pa, where P is Bergman's projection over a bounded domain Ω and a is a function analytic on , detect the length of the boundary of a(Ω). Also we point out the relation of that operator and the spectral asymptotics of a Hankel operator with an anti-analytic symbol.
The Geometry of Quadratic Differential Systems with a Weak Focus of Third Order
Authors: Llibre Jaume , Schlomiuk Dana
Published: December 2010

In this article we determine the global geometry of the planar quadratic differential systems with a weak focus of third order. This class plays a significant role in the context of Hilbert's 16-th problem. Indeed, all examples of quadratic differential systems with at least four limit cycles, were obtained by perturbing a system in this family. We use the algebro-geometric concepts of divisor and zero-cycle to encode global properties of the systems and to give structure to this class. We give a theorem of topological classification of such systems in terms of integer-valued affine invariants. According to the possible values taken by them in this family we obtain a total of 18 topologically distinct phase portraits. We show that inside the class of all quadratic systems with the topology of the coefficients, there exists a neighborhood of the family of quadratic systems with a weak focus of third order and which may have graphics but no polycycle in the sense of [15] and no limit cycle, such that any quadratic system in this neighborhood has at most four limit cycles.
Predual of the Multiplier Algebra of Ap(G) and Amenability
Authors: Miao Tianxuan
Published: December 2010

For a locally compact group G and 1 < p < ∞, let Ap(G) be the Herz-Figà-Talamanca algebra and let PMp(G) be its dual Banach space. For a Banach Ap(G)-module X of PMp(G), we prove that the multiplier space ℳ(Ap(G); X*) is the dual Banach space of QX, where QX is the norm closure of the linear span Ap(G)X of u f for u 2 Ap(G) and f ∈ X in the dual of ℳ(Ap(G); X*). If p = 2 and PFp(G) ⊆ X, then Ap(G)X is closed in X if and only if G is amenable. In particular, we prove that the multiplier algebra MAp(G) of Ap(G) is the dual of Q, where Q is the completion of L1(G) in the ‖ · ‖M-norm. Q is characterized by the following: f ∈ Q if an only if there are ui ∈ Ap(G) and fi ∈ PFp(G) (i = 1; 2, … ) with such that on MAp(G). It is also proved that if Ap(G) is dense in MAp(G) in the associated w*-topology, then the multiplier norm and ‖ · ‖Ap(G)-norm are equivalent on Ap(G) if and only if G is amenable.
Coinvariant Algebras of Finite Subgroups of SL(3;C)
Authors: Gomi Yasushi , Nakamura Iku , Shinoda Ken-ichi
Published: December 2010

For most of the finite subgroups of SL(3; C) we give explicit formulae for the Molien series of the coinvariant algebras, generalizing McKay's formulae [McKay99] for subgroups of SU(2). We also study the G-orbit Hilbert scheme HilbG(C3) for any finite subgroup G of SO(3), which is known to be a minimal (crepant) resolution of the orbit space C3/G. In this case the fiber over the origin of the Hilbert-Chow morphism from HilbG(C3) to C3/G consists of finitely many smooth rational curves, whose planar dual graph is identified with a certain subgraph of the representation graph of G. This is an SO(3) version of the McKay correspondence in the SU(2) case.
The Heat Kernel and Green's Function on a Manifold with Heisenberg Group as Boundary
Authors: Ni Yilong
Published: December 2010

We study the Riemannian Laplace-Beltrami operator L on a Riemannian manifold with Heisenberg group H1 as boundary. We calculate the heat kernel and Green's function for L, and give global and small time estimates of the heat kernel. A class of hypersurfaces in this manifold can be regarded as approximations of H1. We also restrict L to each hypersurface and calculate the corresponding heat kernel and Green's function. We will see that the heat kernel and Green's function converge to the heat kernel and Green's function on the boundary.
Type Decomposition and the Rectangular AFD Property for W*-TRO’s
Authors: Ruan Zhong-Jin
Published: December 2010

We study the type decomposition and the rectangular AFD property for W*-TRO’s. Like von Neumann algebras, every W*-TRO can be uniquely decomposed into the direct sum of W*- TRO's of type I, type II, and type III. We may further considerW*-TRO's of type Im,n with cardinal numbers m and n, and considerW*-TRO's of type IIλ,μ with λ, μ = 1 or ∞. It is shown that every separable stable W*-TRO (which includes type I∞, ∞, type II∞, ∞ and type III) is TRO-isomorphic to a von Neumann algebra. We also introduce the rectangular version of the approximately finite dimensional property for W*-TRO’s. One of our major results is to show that a separable W*-TRO is injective if and only if it is rectangularly approximately finite dimensional. As a consequence of this result, we show that a dual operator space is injective if and only if its operator predual is a rigid rectangular space (equivalently, a rectangular space).
A Berry-Esseen Type Theorem on Nilpotent Covering Graphs
Authors: Ishiwata Satoshi
Published: December 2010

We prove an estimate for the speed of convergence of the transition probability for a symmetric random walk on a nilpotent covering graph. To obtain this estimate, we give a complete proof of the Gaussian bound for the gradient of the Markov kernel.
Regular Embeddings of Generalized Hexagons
Authors: Steinbach Anja , Van Maldeghem Hendrik
Published: December 2010

We classify the generalized hexagons which are laxly embedded in projective space such that the embedding is flat and polarized. Besides the standard examples related to the hexagons defined over the algebraic groups of type G2,3D4and6D4(and occurring in projective dimensions 5, 6, 7), we find new examples in unbounded dimension related to the mixed groups of type G2.
On the Connectedness of Moduli Spaces of Flat Connections over Compact Surfaces
Authors: Ho Nan-Kuo , Melissa Liu Chiu-Chu
Published: December 2010

We study the connectedness of the moduli space of gauge equivalence classes of flat G-connections on a compact orientable surface or a compact nonorientable surface for a class of compact connected Lie groups. This class includes all the compact, connected, simply connected Lie groups, and some non-semisimple classical groups.
On Amenability and Co-Amenability of Algebraic Quantum Groups and Their Corepresentations
Authors: Bédos Erik , Conti Roberto , Tuset Lars
Published: December 2010

We introduce and study several notions of amenability for unitary corepresentations and *-representations of algebraic quantum groups, which may be used to characterize amenability and co-amenability for such quantumgroups. As a background for this study, we investigate the associated tensor C*-categories.
On the Waring–Goldbach Problem: Exceptional Sets for Sums of Cubes and Higher Powers
Authors: Kumchev Angel V.
Published: December 2010

We investigate exceptional sets in theWaring–Goldbach problem. For example, in the cubic case, we show that all but O(N79/84+∊) integers subject to the necessary local conditions can be represented as the sum of five cubes of primes. Furthermore, we develop a new device that leads easily to similar estimates for exceptional sets for sums of fourth and higher powers of primes.
Generalized k-Configurations
Authors: Sabourin Sindi
Published: December 2010

In this paper, we find configurations of points in n-dimensional projective space (Pn) which simultaneously generalize both k-configurations and reduced 0-dimensional complete intersections. Recall that k-configurations in P2 are disjoint unions of distinct points on lines and in Pn are inductively disjoint unions of k-configurations on hyperplanes, subject to certain conditions. Furthermore, the Hilbert function of a k-configuration is determined from those of the smaller k-configurations. We call our generalized constructions kD-configurations, where D = {d1, … , dr} (a set of r positive integers with repetition allowed) is the type of a given complete intersection in Pn. We show that the Hilbert function of any kD-configuration can be obtained from those of smaller kD-configurations. We then provide applications of this result in two different directions, both of which are motivated by corresponding results about k-configurations.
On the Sizes of Gaps in the Fourier Expansion of Modular Forms
Authors: Alkan Emre
Published: December 2010

Let be a cusp form with integer weight k ≥ 2 that is not a linear combination of forms with complex multiplication. For n ≥ 1, let

Concerning bounded values of i f (n) we prove that for ∊ > 0 there exists M = M(∊, f ) such that Using results of Wu, we show that if f is a weight 2 cusp form for an elliptic curve without complex multiplication, then . Using a result of David and Pappalardi, we improve the exponent to for almost all newforms associated to elliptic curves without complex multiplication. Inspired by a classical paper of Selberg, we also investigate i f (n) on the average using well known bounds on the Riemann Zeta function.
Reverse Hypercontractivity for Subharmonic Functions
Authors: Gross Leonard , Grothaus Martin
Published: December 2010

Contractivity and hypercontractivity properties of semigroups are now well understood when the generator, A, is a Dirichlet form operator. It has been shown that in some holomorphic function spaces the semigroup operators, e−tA, can be bounded below from Lp to Lq when p, q and t are suitably related. We will show that such lower boundedness occurs also in spaces of subharmonic functions.
Branching Rules for Principal Series Representations of SL(2) over a p-adic Field
Authors: Nevins Monica
Published: December 2010

We explicitly describe the decomposition into irreducibles of the restriction of the principal series representations of SL(2, k), for k a p-adic field, to each of its two maximal compact subgroups (up to conjugacy). We identify these irreducible subrepresentations in the Kirillov-type classification of Shalika. We go on to explicitly describe the decomposition of the reducible principal series of SL(2, k) in terms of the restrictions of its irreducible constituents to a maximal compact subgroup.
Curvature Estimates in Asymptotically Flat Lorentzian Manifolds
Authors: Finster Felix , Kraus Margarita
Published: December 2010

We consider an asymptotically flat Lorentzian manifold of dimension (1, 3). An inequality is derived which bounds the Riemannian curvature tensor in terms of the ADM energy in the general case with second fundamental form. The inequality quantifies in which sense the Lorentzianmanifold becomes flat in the limit when the ADM energy tends to zero.
Representation of Banach Ideal Spaces and Factorization of Operators
Authors: Berezhnoĭ Evgenii I. , Maligranda Lech
Published: December 2010

Representation theorems are proved for Banach ideal spaces with the Fatou property which are built by the Calderón–Lozanovskiĭ construction. Factorization theorems for operators in spaces more general than the Lebesgue Lpspaces are investigated. It is natural to extend the Gagliardo theorem on the Schur test and the Rubio de Francia theorem on factorization of the Muckenhoupt Ap weights to reflexive Orlicz spaces. However, it turns out that for the scales far fromLp-spaces this is impossible. For the concrete integral operators it is shown that factorization theorems and the Schur test in some reflexive Orlicz spaces are not valid. Representation theorems for the Calderón–Lozanovskiĭ construction are involved in the proofs.
Some Transformations of Hausdorff Moment Sequences and Harmonic Numbers
Authors: Berg Christian , Durán Antonio J.
Published: December 2010

We introduce some non-linear transformations from the set of Hausdorff moment sequences into itself; among them is the one defined by the formula: . We give some examples of Hausdorff moment sequences arising from the transformations and provide the corresponding measures: one of these sequences is the reciprocal of the harmonic numbers .
Cone-Monotone Functions: Differentiability and Continuity
Authors: Borwein Jonathan M. , Wang Xianfu
Published: December 2010

We provide a porosity-based approach to the differentiability and continuity of real-valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone K with non-empty interior. We also show that the set of nowhere K-monotone functions has a σ-porous complement in the space of continuous functions endowed with the uniform metric.
A Symmetric Imprimitivity Theorem for Commuting Proper Actions
Authors: Huef Astrid an , Raeburn Iain , Williams Dana P.
Published: December 2010

We prove a symmetric imprimitivity theoremfor commuting proper actions of locally compact groups H and K on a C*-algebra.
Constructing Representations of Finite Simple Groups and Covers
Authors: Dabbaghian-Abdoly Vahid
Published: December 2010

Let G be a finite group and χ be an irreducible character of G. An efficient and simple method to construct representations of finite groups is applicable whenever G has a subgroup H such that χH has a linear constituent with multiplicity 1. In this paper we show (with a few exceptions) that if G is a simple group or a covering group of a simple group and χ is an irreducible character of G of degree less than 32, then there exists a subgroup H (often a Sylow subgroup) of G such that χH has a linear constituent with multiplicity 1.
Quelques résultats sur les équations axp + byp = cz2
Authors: Ivorra W. , Kraus A.
Published: December 2010

Let p be a prime number ≥ 5 and a, b, c be non zero natural numbers. Using the works of K. Ribet and A. Wiles on the modular representations, we get new results about the description of the primitive solutions of the diophantine equation axp + byp = cz2, in case the product of the prime divisors of abc divides 2ℓ, with ℓ an odd prime number. For instance, under some conditions on a, b, c, we provide a constant f (a, b, c) such that there are no such solutions if p > f (a, b, c). In application, we obtain information concerning the ℚ-rational points of hyperelliptic curves given by the equation y2 = xp + d with d ∈ ℤ.
Convergence of Fourier–Padé Approximants for Stieltjes Functions
Authors: Bello Hernández M. , Mínguez Ceniceros J.
Published: December 2010

We prove convergence of diagonal multipoint Padé approximants of Stieltjes-type functions when a certain moment problem is determinate. This is used for the study of the convergence of Fourier–Padé and nonlinear Fourier–Padé approximants for such type of functions.