bluuebunny/crossref_metadata_2025_split huggingface dataset:
Galois Representations with Non-Surjective Traces
Authors: David Chantal , Kisilevsky Hershy , Pappalardi Francesco 
Published: December 2010

AbstractLet E be an elliptic curve over , and let r be an integer. According to the Lang-Trotter conjecture, the number of primes p such that ap(E) = r is either finite, or is asymptotic to CE,r√x/log x where CE,r is a non-zero constant. A typical example of the former is the case of rational ℓ-torsion, where ap(E) = r is impossible if r ≡ 1 (mod ℓ). We prove in this paper that, when E has a rational ℓ-isogeny and ℓ ≠ 11, the number of primes p such that ap(E) ≡ r (mod ℓ) is finite (for some r modulo ℓ) if and only if E has rational ℓ-torsion over the cyclotomic field (ζℓ). The case ℓ = 11 is special, and is also treated in the paper. We also classify all those occurences.
Quadratic Integers and Coxeter Groups
Authors: Johnson Norman W. , Weiss Asia Ivić 
Published: December 2010

AbstractMatrices whose entries belong to certain rings of algebraic integers can be associated with discrete groups of transformations of inversiven-space or hyperbolic (n+1)-space Hn+1. For smalln, thesemay be Coxeter groups, generated by reflections, or certain subgroups whose generators include direct isometries of Hn+1. We show how linear fractional transformations over rings of rational and (real or imaginary) quadratic integers are related to the symmetry groups of regular tilings of the hyperbolic plane or 3-space. New light is shed on the properties of the rational modular group PSL2(), the Gaussian modular (Picard) group PSL2([i]), and the Eisenstein modular group PSL2([ω]).
A Stochastic Calculus Approach for the Brownian Snake
Authors: Dhersin Jean-Stéphane , Serlet Laurent 
Published: December 2010

AbstractWe study the “Brownian snake” introduced by Le Gall, and also studied by Dynkin, Kuznetsov, Watanabe. We prove that Itô’s formula holds for a wide class of functionals. As a consequence, we give a new proof of the connections between the Brownian snake and super-Brownian motion. We also give a new definition of the Brownian snake as the solution of a well-posed martingale problem. Finally, we construct a modified Brownian snake whose lifetime is driven by a path-dependent stochastic equation. This process gives a representation of some super-processes.
Spectral Problems for Non-Linear Sturm-Liouville Equations with Eigenparameter Dependent Boundary Conditions
Authors: Binding Paul A. , Browne Patrick J. , Watson Bruce A. 
Published: December 2010

AbstractThe nonlinear Sturm-Liouville equation−(pyʹ)ʹ +qy= λ(1 −f)ryon [0, 1]is considered subject to the boundary conditions(ajλ +bj)y(j) = (cjλ +dj)(pyʹ)(j),j= 0, 1.Herea0= 0 =c0andp, r> 0 andqare functions depending on the independent variablexalone, whilefdepends onx, yandyʹ. Results are given on existence and location of sets of (λ,y) bifurcating from the linearized eigenvalues, and for whichyhas prescribed oscillation count, and on completeness of theyin an appropriate sense.
Sums of Two Squares in Short Intervals
Authors: Balog Antal , Wooley Trevor D. 
Published: December 2010

AbstractLetdenote the set of integers representable as a sum of two squares. Sincecan be described as the unsifted elements of a sieving process of positive dimension, it is to be expected thathasmany properties in common with the set of prime numbers. In this paper we exhibit “unexpected irregularities” in the distribution of sums of two squares in short intervals, a phenomenon analogous to that discovered by Maier, over a decade ago, in the distribution of prime numbers. To be precise, we show that there are infinitely many short intervals containing considerably more elements ofthan expected, and infinitely many intervals containing considerably fewer than expected.
Le problème de Neumann pour certaines équations du type de Monge-Ampère sur une variété riemannienne
Authors: Hanani Abdellah 
Published: December 2010

AbstractLet (Mn, g) be a strictly convex riemannian manifold with C∞ boundary. We prove the existence of classical solution for the nonlinear elliptic partial differential equation of Monge-Ampère: det in M with a Neumann condition on the boundary of the form , where is an everywhere strictly positive function satisfying some assumptions, ν stands for the unit normal vector field and is a non-decreasing function in u.
The Dunford-Pettis Property for Symmetric Spaces
Authors: Kamińska Anna , Mastyło Mieczysław 
Published: December 2010

AbstractA complete description of symmetric spaces on a separable measure space with the Dunford-Pettis property is given. It is shown that ℓ1, c0 and ℓ∞ are the only symmetric sequence spaces with the Dunford- Pettis property, and that in the class of symmetric spaces on (0, α), 0 < α ≤ ∞, the only spaces with the Dunford-Pettis property are L1, L∞, L1 ∩ L∞, L1 + L∞, (L∞)◦ and (L1 + L∞)◦, where X◦ denotes the norm closure of L1 ∩ L∞ in X. It is also proved that all Banach dual spaces of L1 ∩ L∞ and L1 + L∞ have the Dunford-Pettis property. New examples of Banach spaces showing that the Dunford-Pettis property is not a three-space property are also presented. As applications we obtain that the spaces (L1 + L∞)◦ and (L∞)◦ have a unique symmetric structure, and we get a characterization of the Dunford-Pettis property of some Köthe-Bochner spaces.
Complex Monge-Ampère Measures of Plurisubharmonic Functions with Bounded Values Near the Boundary
Authors: Xing Yang 
Published: December 2010

AbstractWe give a characterization of bounded plurisubharmonic functions by using their complex Monge-Ampère measures. This implies a both necessary and sufficient condition for a positive measure to be complex Monge-Ampère measure of some bounded plurisubharmonic function.
On the Curves Associated to Certain Rings of Automorphic Forms
Authors: Khuri-Makdisi Kamal 
Published: December 2010

AbstractIn a 1987 paper, Gross introduced certain curves associated to a definite quaternion algebra B over Q; he then proved an analog of his result with Zagier for these curves. In Gross’ paper, the curves were defined in a somewhat ad hoc manner. In this article, we present an interpretation of these curves as projective varieties arising from graded rings of automorphic forms on B×, analogously to the construction in the Satake compactification. To define such graded rings, one needs to introduce a “multiplication” of automorphic forms that arises from the representation ring of B×. The resulting curves are unions of projective lines equipped with a collection of Hecke correspondences. They parametrize two-dimensional complex tori with quaternionic multiplication. In general, these complex tori are not abelian varieties; they are algebraic precisely when they correspond to CM points on these curves, and are thus isogenous to a product E × E, where E is an elliptic curve with complex multiplication. For these CM points one can make a relation between the action of the p-th Hecke operator and Frobenius at p, similar to the well-known congruence relation of Eichler and Shimura.
Bivariate Polynomials of Least Deviation from Zero
Authors: Bojanov Borislav D. , Haußmann Werner , Nikolov Geno P. 
Published: December 2010

AbstractBivariate polynomials with a fixed leading term xmyn, which deviate least fromzero in the uniform or L2-norm on the unit disk D (resp. a triangle) are given explicitly. A similar problem in Lp, 1 ≤ p ≤ ∞, is studied on D in the set of products of linear polynomials.
K-Theory of Non-Commutative Spheres Arising from the Fourier Automorphism
Authors: Walters Samuel G. 
Published: December 2010

AbstractFor a dense Gδ set of real parameters θ in [0, 1] (containing the rationals) it is shown that the group K0(Aθ ⋊σ) is isomorphic to , where Aθ is the rotation C*-algebra generated by unitaries U, V satisfying VU = e2πiθUV and σ is the Fourier automorphism of Aθ defined by σ(U) = V, σ(V) = U−1. More precisely, an explicit basis for K0 consisting of nine canonical modules is given. (A slight generalization of this result is also obtained for certain separable continuous fields of unital C*-algebras over [0, 1].) The Connes Chern character ch: K0(Aθ ⋊σ) → Hev (Aθ ⋊σ)* is shown to be injective for a dense Gδ set of parameters θ. The main computational tool in this paper is a group homomorphism T: K0(Aθ ⋊σ) → obtained from the Connes Chern character by restricting the functionals in its codomain to a certain nine-dimensional subspace of Hev (Aθ ⋊σ). The range of T is fully determined for each θ. (We conjecture that this subspace is all of Hev.)
Inverse Problems for Partition Functions
Authors: Yang Yifan 
Published: December 2010

AbstractLet pw(n) be the weighted partition function defined by the generating function , where w(m) is a non-negative arithmetic function. Let be the summatory functions for pw(n) and w(n), respectively. Generalizing results of G. A. Freiman and E. E. Kohlbecker, we show that, for a large class of functions Φ(u) and λ(u), an estimate for Pw(u) of the formlog Pw(u) = Φ(u){1 + Ou(1/λ(u))} (u→∞) implies an estimate forNw(u) of the formNw(u) = Φ*(u){1+O(1/ log ƛ(u))} (u→∞) with a suitable function Φ*(u) defined in terms of Φ(u). We apply this result and related results to obtain characterizations of the Riemann Hypothesis and the Generalized Riemann Hypothesis in terms of the asymptotic behavior of certain weighted partition functions.
Sur le comportement, par torsion, des facteurs epsilon de paires
Authors: Bushnell Colin J. , Henniart Guy 
Published: December 2010

RésuméSoient$F$un corps commutatif localement compact non archimédien et$\psi$un caractère additif non trivial de$F$. Soient$n$et${n}'$deux entiers distincts, supérieurs à 1. Soient$\pi$et${\pi }'$des représentations irréductibles supercuspidales de$\text{G}{{\text{L}}_{n}}\left( F \right)$,$\text{G}{{\text{L}}_{{{n}'}}}\left( F \right)$respectivement. Nous prouvons qu’il existe un élément$c=c\left( \pi ,{\pi }',\psi \right)$de${{F}^{\times }}$tel que pour tout quasicaractère modéré$\mathcal{X}$de${{F}^{\times }}$on ait$\mathcal{E}\left( \chi \pi \times {\pi }',s,\psi \right)=\chi {{\left( c \right)}^{-1}}\mathcal{E}\left( \pi \times {\pi }',s,\psi \right)$. Nous examinons aussi certains cas où$n={n}',{\pi }'={{\pi }^{\text{v}}}$. Les résultats obtenus forment une étape vers une démonstration de la conjecture de Langlands pour$F$, qui ne fasse pas appel à la géométrie des variétés modulaires, de Shimura ou de Drinfeld.
Comparisons of General Linear Groups and their Metaplectic Coverings I
Authors: Mezo Paul 
Published: December 2010

AbstractWe prepare for a comparison of global trace formulas of general linear groups and their metaplectic coverings. In particular, we generalize the local metaplectic correspondence of Flicker and Kazhdan and describe the terms expected to appear in the invariant trace formulas of the above covering groups. The conjectural trace formulas are then placed into a form suitable for comparison.
Spaces of Whitney Functions on Cantor-Type Sets
Authors: Arslan Bora , Goncharov Alexander P. , Kocatepe Mefharet 
Published: December 2010

AbstractWe introduce the concept of logarithmic dimension of a compact set. In terms of this magnitude, the extension property and the diametral dimension of spaces Ɛ(K) can be described for Cantor-type compact sets.
Slim Exceptional Sets for Sums of Cubes
Authors: Wooley Trevor D. 
Published: December 2010

AbstractWe investigate exceptional sets associated with various additive problems involving sums of cubes. By developing a method wherein an exponential sum over the set of exceptions is employed explicitly within the Hardy-Littlewood method, we are better able to exploit excess variables. By way of illustration, we show that the number of odd integers not divisible by 9, and not exceeding X, that fail to have a representation as the sum of 7 cubes of prime numbers, is O(X23/36+ε). For sums of eight cubes of prime numbers, the corresponding number of exceptional integers is O(X11/36+ε).
Théorème de Voronoï dans les espaces symétriques
Authors: Akrout H. 
Published: December 2010

RésuméOn démontre un théorème de Voronoï (caractérisation des maxima locaux de l’invariant d’Hermite) pour les familles de réseaux paramétrées par les espaces symétriques irréductibles non exceptionnels de type non compact.
Diagonals and Partial Diagonals of Sum of Matrices
Authors: Li Chi-Kwong , Poon Yiu-Tung 
Published: December 2010

AbstractGiven a matrix A, let (A) denote the orbit of A under a certain group action such as(1)U(m) ⊗ U(n) acting on m × n complex matrices A by (U, V) * A = UAVt,(2)O(m) ⊗ O(n) or SO(m) ⊗ SO(n) acting on m × n real matrices A by (U, V) * A = UAVt,(3)U(n) acting on n × n complex symmetric or skew-symmetric matrices A by U * A = UAUt,(4)O(n) or SO(n) acting on n × n real symmetric or skew-symmetric matrices A by U * A = UAUt.Denote bythe joint orbit of the matrices A1, … , Ak. We study the set of diagonals or partial diagonals of matrices in (A1, … , Ak), i.e., the set of vectors (d1, … , dr) whose entries lie in the (1, j1), … , (r, jr) positions of a matrix in (A1, … , Ak) for some distinct column indices j1, … , jr . In many cases, complete description of these sets is given in terms of the inequalities involving the singular values of A1, … , Ak. We also characterize those extreme matrices for which the equality cases hold. Furthermore, some convexity properties of the joint orbits are considered. These extend many classical results on matrix inequalities, and answer some questions by Miranda. Related results on the joint orbit (A1, … , Ak) of complex Hermitian matrices under the action of unitary similarities are also discussed.
Resonances for Slowly Varying Perturbations of a Periodic Schrödinger Operator
Authors: Dimassi Mouez 
Published: December 2010

AbstractWe study the resonances of the operator . Here V is a periodic potential, φ a decreasing perturbation and h a small positive constant. We prove the existence of shape resonances near the edges of the spectral bands of , and we give its asymptotic expansions in powers of .
On the Injectivity of C1 Maps of the Real Plane
Authors: Cobo Milton , Gutierrez Carlos , Llibre Jaume 
Published: December 2010

AbstractLet X : → be a C1 map. Denote by Spec(X) the set of (complex) eigenvalues of DXp when p varies in . If there exists ∊ > 0 such that Spec(X) ∩ (− ∊, ∊) = ∅, then X is injective. Some applications of this result to the real Keller Jacobian conjecture are discussed.
Besov Spaces and Hausdorff Dimension For Some Carnot-Carathéodory Metric Spaces
Authors: Skrzypczak Leszek 
Published: December 2010

AbstractWe regard a system of left invariant vector fieldssatisfying the Hörmander condition and the related Carnot-Carathéodory metric on a unimodular Lie group G. We define Besov spaces corresponding to the sub-Laplacianboth with positive and negative smoothness. The atomic decomposition of the spaces is given. In consequence we get the distributional characterization of the Hausdorff dimension of Borel subsets with the Haar measure zero.
*-Subvarieties of the Variety Generated by
Authors: Benanti Francesca , Di Vincenzo Onofrio M. , Nardozza Vincenzo 
Published: December 2010

AbstractLet be a field of characteristic zero, and * = t the transpose involution for the matrix algebra M2(). Let be a proper subvariety of the variety of algebras with involution generated by . We define two sequences of algebras with involution Rp, Sq, where p, q ∊ . Then we show that T*() and T*(Rp ⊕ Sq) are *-asymptotically equivalent for suitable p, q.
Some Convexity Features Associated with Unitary Orbits
Authors: Choi Man-Duen , Li Chi-Kwong , Poon Yiu-Tung 
Published: December 2010

AbstractLet be the real linear space of n × n complex Hermitian matrices. The unitary (similarity) orbit of C ∈ is the collection of all matrices unitarily similar to C. We characterize those C ∈ such that every matrix in the convex hull of can be written as the average of two matrices in . The result is used to study spectral properties of submatrices of matrices in , the convexity of images of under linear transformations, and some related questions concerning the joint C-numerical range of Hermitian matrices. Analogous results on real symmetric matrices are also discussed.
On the Zariski-van Kampen Theorem
Authors: Shimada Ichiro 
Published: December 2010

AbstractLet f : E → B be a dominant morphism, where E and B are smooth irreducible complex quasi-projective varieties, and let Fb be the general fiber of f. We present conditions under which the homomorphism π1(Fb) → π1(E) induced by the inclusion is injective.
Pair Correlation of Squares in p-Adic Fields
Authors: Zaharescu Alexandru 
Published: December 2010

AbstractLet p be an odd prime number, K a p-adic field of degree r over Qp, O the ring of integers in K, B = {β1,…,βr} an integral basis of K over Qp, u a unit in O and consider sets of the form 𝒩 = {n1β1 + … + nrβr : 1 ≤ nj ≤ Nj, 1 ≤ j ≤ r}. We show under certain growth conditions that the pair correlation of {uz2 : z ∊ 𝒩} becomes Poissonian.
Une formule de Riemann-Roch équivariante pour les courbes
Authors: Borne Niels 
Published: December 2010

AbstractSoitGun groupe fini agissant sur une courbe algébrique projective et lisseXsur un corps algébriquement closk. Dans cet article, on donne une formule de Riemann-Roch pour la caractéristique d'Euler équivariante d'unG-faisceau inversible ℒ, à valeurs dans l'anneauRk(G) des caractères du groupeG. La formule donnée a un bon comportement fonctoriel en ce sens qu'elle relève la formule classique le long du morphisme dim:Rk(G) → ℤ, et est valable même pour une action sauvage. En guise d'application, on montre comment calculer explicitement le caractère de l'espace des sections globales d'une large classe deG-faisceaux inversibles, en s'attardant sur le cas particulier délicat du faisceau des différentielles sur la courbe.
Almost-Free E-Rings of Cardinality ℵ1
Authors: Göbel Rüdiger , Shelah Saharon , Strüngmann Lutz 
Published: December 2010

AbstractAn E-ring is a unital ring R such that every endomorphism of the underlying abelian group R+ is multiplication by some ring element. The existence of almost-free E-rings of cardinality greater than 2ℵ0 is undecidable in ZFC. While they exist in Gödel's universe, they do not exist in other models of set theory. For a regular cardinal ℵ1 ≤ λ 2ℵ0 we construct E-rings of cardinality λ in ZFC which have ℵ1-free additive structure. For λ = ℵ1 we therefore obtain the existence of almost-free E-rings of cardinality ℵ1 in ZFC.
Homology TQFT's and the Alexander–Reidemeister Invariant of 3-Manifolds via Hopf Algebras and Skein Theory
Authors: Kerler Thomas 
Published: December 2010

AbstractWe develop an explicit skein-theoretical algorithm to compute the Alexander polynomial of a 3-manifold from a surgery presentation employing the methods used in the construction of quantum invariants of 3-manifolds. As a prerequisite we establish and prove a rather unexpected equivalence between the topological quantum field theory constructed by Frohman and Nicas using the homology ofU(1)-representation varieties on the one side and the combinatorially constructed Hennings TQFT based on the quasitriangular Hopf algebra= ℤ/2 n ⋊ Λ* ℝ2on the other side. We find that both TQFT's are SL(2; ℝ)-equivariant functors and, as such, are isomorphic. The SL(2; ℝ)-action in the Hennings construction comes from the natural action onand in the case of the Frohman–Nicas theory from the Hard–Lefschetz decomposition of theU(1)-moduli spaces given that they are naturally Kähler. The irreducible components of this TQFT, corresponding to simple representations of SL(2; ℤ) and Sp(2g; ℤ), thus yield a large family of homological TQFT's by taking sums and products. We give several examples of TQFT's and invariants that appear to fit into this family, such as Milnor and Reidemeister Torsion, Seiberg–Witten theories, Casson type theories for homology circlesà laDonaldson, higher rank gauge theories following Frohman and Nicas, and the ℤ=pℤ reductions of Reshetikhin.Turaev theories over the cyclotomic integers ℤ[ζp]. We also conjecture that the Hennings TQFT for quantum-sl2is the product of the Reshetikhin–Turaev TQFT and such a homological TQFT.
An Ordering for Groups of Pure Braids and Fibre-Type Hyperplane Arrangements
Authors: Kim Djun Maximilian , Rolfsen Dale 
Published: December 2010

AbstractWe define a total ordering of the pure braid groups which is invariant under multiplication on both sides. This ordering is natural in several respects. Moreover, it well-orders the pure braids which are positive in the sense of Garside. The ordering is defined using a combination of Artin's combing technique and the Magnus expansion of free groups, and is explicit and algorithmic.By contrast, the full braid groups (on 3 or more strings) can be ordered in such a way as to be invariant on one side or the other, but not both simultaneously. Finally, we remark that the same type of ordering can be applied to the fundamental groups of certain complex hyperplane arrangements, a direct generalization of the pure braid groups.
Hypergeometric Abelian Varieties
Authors: Archinard Natália 
Published: December 2010

AbstractIn this paper, we construct abelian varieties associated to Gauss’ and Appell–Lauricella hypergeometric series. Abelian varieties of this kind and the algebraic curves we define to construct them were considered by several authors in settings ranging from monodromy groups (Deligne, Mostow), exceptional sets (Cohen, Wolfart, Wüstholz), modular embeddings (Cohen, Wolfart) to CM-type (Cohen, Shiga, Wolfart) and modularity (Darmon). Our contribution is to provide a complete, explicit and self-contained geometric construction.
Polar Homology
Authors: Khesin Boris , Rosly Alexei 
Published: December 2010

AbstractFor complex projective manifolds we introduce polar homology groups, which are holomorphic analogues of the homology groups in topology. The polar k-chains are subvarieties of complex dimension k with meromorphic forms on them, while the boundary operator is defined by taking the polar divisor and the Poincaré residue on it. One can also define the corresponding analogues for the intersection and linking numbers of complex submanifolds, which have the properties similar to those of the corresponding topological notions.
Decay of Mean Values of Multiplicative Functions
Authors: Granville Andrew , Soundararajan K. 
Published: December 2010

AbstractFor given multiplicative functionf, with |f(n)| ≤ 1 for alln, we are interested in how fast its mean value (1/x) Σn≤xf(n) converges. Halász showed that this depends on the minimumM(overy∈ ℝ) of Σp≤x(1 – Re(f(p)p–iy)/p, and subsequent authors gave the upper bound ⪡ (1 +M)e–M. For many applications it is necessary to have explicit constants in this and various related bounds, and we provide these via our own variant of the Halász-Montgomery lemma (in fact the constant we give is best possible up to a factor of 10). We also develop a new type of hybrid bound in terms of the location of the absolute value ofythat minimizes the sum above. As one application we give bounds for the least representatives of the cosets of thek-th powers modp.