bluuebunny/crossref_metadata_2025_split huggingface dataset:
Partial Euler Products on the Critical Line
Authors: Conrad Keith 
Published: December 2010

AbstractThe initial version of the Birch and Swinnerton-Dyer conjecture concerned asymptotics for partial Euler products for an elliptic curve L-function at s = 1. Goldfeld later proved that these asymptotics imply the Riemann hypothesis for the L-function and that the constant in the asymptotics has an unexpected factor of. We extend Goldfeld's theorem to an analysis of partial Euler products for a typical L-function along its critical line. The general phenomenon is related to second moments, while the asymptotic behavior (over number fields) is proved to be equivalent to a condition that in a precise sense seemsmuch deeper than the Riemann hypothesis. Over function fields, the Euler product asymptotics can sometimes be proved unconditionally.
On Local L-Functions and Normalized Intertwining Operators
Authors: Kim Henry H. 
Published: December 2010

AbstractIn this paper we make explicit all L-functions in the Langlands–Shahidi method which appear as normalizing factors of global intertwining operators in the constant term of the Eisenstein series. We prove, in many cases, the conjecture of Shahidi regarding the holomorphy of the local L-functions. We also prove that the normalized local intertwining operators are holomorphic and non-vaninishing for Re(s) ≥ 1/2 in many cases. These local results are essential in global applications such as Langlands functoriality, residual spectrumand determining poles of automorphic L-functions.
On the Structure of the Spreading Models of a Banach Space
Authors: Androulakis G. , Odell E. , Schlumprecht Th. , Tomczak-Jaegermann N. 
Published: December 2010

AbstractWe study some questions concerning the structure of the set of spreading models of a separable infinite-dimensional Banach space X. In particular we give an example of a reflexive X so that all spreading models of X contain ℓ1 but none of them is isomorphic to ℓ1. We also prove that for any countable set C of spreading models generated by weakly null sequences there is a spreading model generated by a weakly null sequence which dominates each element of C. In certain cases this ensures that X admits, for each α < ω1, a spreading model such that if α < β then is dominated by (and not equivalent to) . Some applications of these ideas are used to give sufficient conditions on a Banach space for the existence of a subspace and an operator defined on the subspace, which is not a compact perturbation of a multiple of the inclusion map.
Models in Which Every Nonmeager Set is Nonmeager in a Nowhere Dense Cantor Set
Authors: Burke Maxim R. , Miller Arnold W. 
Published: December 2010

AbstractWe prove that it is relatively consistent with ZFC that in any perfect Polish space, for every nonmeager set A there exists a nowhere dense Cantor set C such that A ∩ C is nonmeager in C. We also examine variants of this result and establish a measure theoretic analog.
The Square Sieve and the Lang–Trotter Conjecture
Authors: Cojocaru Alina Carmen , Fouvry Etienne , Murty M. Ram 
Published: December 2010

AbstractLet E be an elliptic curve defined over ℚ and without complex multiplication. Let K be a fixed imaginary quadratic field. We find nontrivial upper bounds for the number of ordinary primes p ≤ x for which ℚ(πp) = K, where πp denotes the Frobenius endomorphism of E at p. More precisely, under a generalized Riemann hypothesis we show that this number is OE(x17/18 log x), and unconditionally we show that this number is We also prove that the number of imaginary quadratic fields K, with −disc K ≤ x and of the form K = ℚ(πp), is ≫E log log log x for x ≥ x0(E). These results represent progress towards a 1976 Lang–Trotter conjecture.
Strictly Singular and Cosingular Multiplications
Authors: Lindström Mikael , Saksman Eero , Tylli Hans-Olav 
Published: December 2010

AbstractLet L(X) be the space of bounded linear operators on the Banach space X. We study the strict singularity and cosingularity of the two-sidedmultiplication operators S ↦ ASB on L(X), where A, B ∈ L(X) are fixed bounded operators and X is a classical Banach space. Let 1 < p < ∞and p ≠ 2. Our main result establishes that the multiplication S ↦ ASB is strictly singular on L(Lp(0, 1)) if and only if the non-zero operators A, B ∈ L(Lp(0, 1)) are strictly singular. We also discuss the case where X is a L1- or a L∞-space, as well as several other relevant examples.
A Semilinear Problem for the Heisenberg Laplacian on Unbounded Domains
Authors: Maad Sara 
Published: December 2010

AbstractWe study the semilinear equationwhere is an unbounded domain of the Heisenberg group . The space is the Heisenberg analogue of the Sobolev space . The function is supposed to be odd in u, continuous and satisfy some (superlinear but subcritical) growth conditions. The operator ΔH is the subelliptic Laplacian on the Heisenberg group. We give a condition on Ω which implies the existence of infinitely many solutions of the above equation. In the proof we rewrite the equation as a variational problem, and show that the corresponding functional satisfies the Palais–Smale condition. This might be quite surprising since we deal with domains which are far frombounded. The technique we use rests on a compactness argument and the maximum principle.
Multiplicity Results for Nonlinear Neumann Problems
Authors: Filippakis Michael , Gasiński Leszek , Papageorgiou Nikolaos S. 
Published: December 2010

AbstractIn this paper we study nonlinear elliptic problems of Neumann type driven by the p-Laplacian differential operator. We look for situations guaranteeing the existence of multiple solutions. First we study problems which are strongly resonant at infinity at the first (zero) eigenvalue. We prove five multiplicity results, four for problems with nonsmooth potential and one for problems with a C1-potential. In the last part, for nonsmooth problems in which the potential eventually exhibits a strict super-p-growth under a symmetry condition, we prove the existence of infinitely many pairs of nontrivial solutions. Our approach is variational based on the critical point theory for nonsmooth functionals. Also we present some results concerning the first two elements of the spectrum of the negative p-Laplacian with Neumann boundary condition.
Singular Integrals on Product Spaces Related to the Carleson Operator
Authors: Prestini Elena 
Published: December 2010

AbstractWe prove Lp(T2) boundedness, 1 < p ≤ 2, of variable coefficients singular integrals that generalize the double Hilbert transform and present two phases that may be of very rough nature. These operators are involved in problems of a.e. convergence of double Fourier series, likely in the role played by the Hilbert transform in the proofs of a.e. convergence of one dimensional Fourier series. The proof due to C.Fefferman provides a basis for our method.
Partie imaginaire des résonances de Rayleigh dans le cas d'une boule
Authors: Gamblin Didier 
Published: December 2010

RésuméNous étudions les résonances de Rayleigh créées par une boule en dimension deux et trois. Nous savons qu’elles convergent exponentiellement vite vers l’axe réel. Nous calculons exactement les fonctions résonantes associées puis nous les estimons asymptotiquement en fonction de la partie réelle des résonances. L’application de la formule de Green nous donne alors le taux de décroissance exponentielle de la partie imaginaire des résonances.
Cohomology Pairings on the Symplectic Reduction of Products
Authors: Goldin R. F. , Martin S. 
Published: December 2010

AbstractLet M be the product of two compact Hamiltonian T-spaces X and Y . We present a formula for evaluating integrals on the symplectic reduction of M by the diagonal T action. At every regular value of the moment map for X × Y, the integral is the convolution of two distributions associated to the symplectic reductions of X by T and of Y by T. Several examples illustrate the computational strength of this relationship. We also prove a linear analogue which can be used to find cohomology pairings on toric orbifolds.
On Pointwise Estimates of Positive Definite Functions With Given Support
Authors: Kolountzakis Mihail N. , Révész Szilárd Gy. 
Published: December 2010

AbstractThe following problem has been suggested by Paul Turán. Let Ω be a symmetric convex body in the Euclidean space ℝd or in the torus . Then, what is the largest possible value of the integral of positive definite functions that are supported in Ω and normalized with the value 1 at the origin? From this, Arestov, Berdysheva and Berens arrived at the analogous pointwise extremal problem for intervals in ℝ. That is, under the same conditions and normalizations, the supremum of possible function values at z is to be found for any given point z ∈ Ω. However, it turns out that the problem for the real line has already been solved by Boas and Kac, who gave several proofs and also mentioned possible extensions to ℝd and to non-convex domains as well.Here we present another approach to the problem, giving the solution in ℝd and for several cases in . Actually, we elaborate on the fact that the problemis essentially one-dimensional and investigate non-convex open domains as well. We show that the extremal problems are equivalent to some more familiar ones concerning trigonometric polynomials, and thus find the extremal values for a few cases. An analysis of the relationship between the problem for ℝd and that for is given, showing that the former case is just the limiting case of the latter. Thus the hierarchy of difficulty is established, so that extremal problems for trigonometric polynomials gain renewed recognition.
Apolar Schemes of Algebraic Forms
Authors: Chipalkatti Jaydeep 
Published: December 2010

AbstractThis is a note on the classical Waring's problem for algebraic forms. Fix integers (n, d, r, s), and let ∧ be a general r-dimensional subspace of degree d homogeneous polynomials in n+1 variables. Let denote the variety of s-sided polar polyhedra of ∧. We carry out a case-by-case study of the structure of for several specific values of (n, d, r, s). In the first batch of examples, is shown to be a rational variety. In the second batch, is a finite set of which we calculate the cardinality.
On the One-Level Density Conjecture for Quadratic Dirichlet L-Functions
Authors: Özlük A. E. , Snyder C. 
Published: December 2010

AbstractIn a previous article, we studied the distribution of “low–lying” zeros of the family of quadratic Dirichlet L–functions assuming the Generalized Riemann Hypothesis for all Dirichlet L–functions. Even with this very strong assumption, we were limited to using weight functions whose Fourier transforms are supported in the interval (–2, 2). However, it is widely believed that this restriction may be removed, and this leads to what has become known as the One-Level Density Conjecture for the zeros of this family of quadratic L-functions. In this note, wemake use of Weil's explicit formula as modified by Besenfelder to prove an analogue of this conjecture.
Holomorphic Generation of Continuous Inverse Algebras
Authors: Biller Harald 
Published: December 2010

AbstractWe study complex commutative Banach algebras (and, more generally, continuous inverse algebras) in which the holomorphic functions of a fixedn-tuple of elements are dense. In particular, we characterize the compact subsets of ℂnwhich appear as joint spectra of suchn-tuples. The characterization is compared with several established notions of holomorphic convexity by means of approximation conditions.
Endomorphism Rings of Finite Global Dimension
Authors: Leuschke Graham J. 
Published: December 2010

AbstractFor a commutative local ring R, consider (noncommutative) R-algebras Λ of the form Λ = EndR(M) where M is a reflexive R-module with nonzero free direct summand. Such algebras Λ of finite global dimension can be viewed as potential substitutes for, or analogues of, a resolution of singularities of Spec R. For example, Van den Bergh has shown that a three-dimensional Gorenstein normal ℂ-algebra with isolated terminal singularities has a crepant resolution of singularities if and only if it has such an algebra Λ with finite global dimension and which is maximal Cohen–Macaulay over R (a “noncommutative crepant resolution of singularities”). We produce algebras Λ = EndR(M) having finite global dimension in two contexts: when R is a reduced one-dimensional complete local ring, or when R is a Cohen–Macaulay local ring of finite Cohen–Macaulay type. If in the latter case R is Gorenstein, then the construction gives a noncommutative crepant resolution of singularities in the sense of Van den Bergh.
Zeta Functions of Supersingular Curves of Genus 2
Authors: Maisner Daniel , Nart Enric 
Published: December 2010

AbstractWe determine which isogeny classes of supersingular abelian surfaces over a finite field k of characteristic 2 contain jacobians. We deal with this problem in a direct way by computing explicitly the zeta function of all supersingular curves of genus 2. Our procedure is constructive, so that we are able to exhibit curves with prescribed zeta function and find formulas for the number of curves, up to k-isomorphism, leading to the same zeta function.
On Cabled Knots and Vassiliev Invariants (Not) Contained in Knot Polynomials
Authors: Stoimenow A. 
Published: December 2010

AbstractIt is known that the Brandt–Lickorish–Millett–Ho polynomialQcontains Casson's knot invariant. Whether there are (essentially) other Vassiliev knot invariants obtainable fromQis an open problem. We show that this is not so up to degree 9. We also give the (apparently) first examples of knots not distinguished by 2-cable HOMFLY polynomials which are not mutants. Our calculations provide evidence of a negative answer to the question whether Vassiliev knot invariants of degreed≤ 10 are determined by the HOMFLY and Kauffman polynomials and their 2-cables, and for the existence of algebras of such Vassiliev invariants not isomorphic to the algebras of their weight systems.
SLn, Orthogonality Relations and Transfer
Authors: Badulescu Alexandru Ioan 
Published: December 2010

AbstractLet π be a square integrable representation of G′ = SLn(D), with D a central division algebra of finite dimension over a local field F of non-zero characteristic. We prove that, on the elliptic set, the character of π equals the complex conjugate of the orbital integral of one of the pseudocoefficients of π. We prove also the orthogonality relations for characters of square integrable representations of G′. We prove the stable transfer of orbital integrals between SLn(F) and its inner forms.
Radical Ideals in Valuation Domains
Authors: van den Berg John E. 
Published: December 2010

AbstractAn idealIof a ringRis called a radical ideal ifI= ℛ(R) where ℛ is a radical in the sense of Kurosh–Amitsur. The main theorem of this paper asserts that ifRis a valuation domain, then a proper idealIofRis a radical ideal if and only ifIis a distinguished ideal ofR(the latter property means that ifJandKare ideals ofRsuch thatJ⊂I⊂Kthen we cannot haveI/J≅K/Ias rings) and that such an ideal is necessarily prime. Examples are exhibited which show that, unlike prime ideals, distinguished ideals are not characterizable in terms of a property of the underlying value group of the valuation domain.
The Ground State Problem for a Quantum Hamiltonian Model Describing Friction
Authors: Bruneau Laurent 
Published: December 2010

AbstractIn this paper, we consider the quantum version of a Hamiltonian model describing friction. This model consists of a particle which interacts with a bosonic reservoir representing a homogeneous medium through which the particle moves. We show that if the particle is confined, then the Hamiltonian admits a ground state if and only if a suitable infrared condition is satisfied. The latter is violated in the case of linear friction, but satisfied when the friction force is proportional to a higher power of the particle speed.
Quotients jacobiens : une approche algébrique
Authors: Reydy Carine 
Published: December 2010

RésuméLe diagramme d’Eisenbud et Neumann d’un germe est un arbre qui représente ce germe et permet d’en calculer les invariants. On donne une démonstration algébrique d’un résultat caract érisant l’ensemble des quotients jacobiens d’un germe d’application (f, g) à partir du diagramme d’Eisenbud et Neumann de fg.
On a Pointwise Construction of the Lemniscate
Authors: Blum Richard 
Published: December 2010

The writer of the following lines is aware of the possibility that the property discussed below is not a new discovery. He will, of course, be grateful to any reader who will provide him with bibliographical references.It is well known-that the nine point circle of a triangle is tangent to the 4 contact (i.e. the inscribed and the escribed) circles. Given two tangent circles and we propose to find the locus of vertices of the triangles (Δ) which admit as their nine point circle and as one of their contact circles.
On the Index of a Quadratic Form
Authors: Wild Jonathan 
Published: December 2010

Given a vector space V = {x, y, ...} over an arbitrary field. In V a symmetric bilinear form (x,y) i s given. A subspace W is called totally isotropic [t.i.] if (x,y) = 0 for every pair x W, y W.Let Vn and Vm be two t.i. subspaces of V; n < m. Lower indices always indicate dimensions. It is a well known and fundamental fact of analytic geometry that there exists a t.i. subspace Wm of V containing Vn [cf. Dieudonné: Les Groupes classiques , P. 18]. As no simple direct proof seems to be available, we propose to supply one.
On a Normal Form of the Orthogonal Transformation III
Authors: Zassenhaus Hans 
Published: December 2010

Under the assumptions of case of theorem 1 we derive from (3.32) the matrix equationso that there corresponds the matrix B to the bilinear form4.1on the linear space4.2and fP,μ, is symmetric if ɛ = (-1)μ+1, anti-symmetric if ɛ = (-1)μ.The last statement remains true in the case a) if P is symmetric irreducible because in that case fP,μ is 0.
A Finite Analogue of the Goldbach Problem
Authors: Dixon J. D. 
Published: December 2010

E. Cohen [1], [2] has considered an analogue of the famous Goldbach problem in certain finite rings. In the following another analogue is considered in the ring Jn of residue classes over the integers modulo n.As 'primes' in Jn we take all residue classes coprime to n. That is, all elements p ϵ Jn which are not factors of zero in Jn. We denote this set by Rn.
A Geometric Model for the Generalized Symmetric Group
Authors: Johnson Norman W. 
Published: December 2010

The generalized symmetric group S(n, m) consists of all permutations of mn symbols commutative withSince each cycle Qi= (1i2i… mi) is of order m, there are mnpermutations within the n cycles, generating an invariant subgroup Q of order mn. Also, there are n! ways of permuting the cycles among themselves, by transformationswhere i1, i2, …, inare the symbols 1, 2, …, n in some order [5, p. 39]. The permutations W* form a subgroup Sn* of order n!, isomorphic to the symmetric group Sn.
On an Inversion Operator for the Fourier Transformation
Authors: Rooney P. G. 
Published: December 2010

In an earlier paper [1] we presented a representation theory for the Fourier transformation defined by1.1for functions f in certain function spaces. This theory made use of an operator1.2where k = 1, 2,…, and it was stated without proof that this operator is an inversion operator for the Fourier transformation; that is, that under certain conditions1.3
A Lemma on Continuous Functions
Authors: Lipman J. 
Published: December 2010

The point of this note is to get a lemma which is useful in treating homotopy between paths in a topological space [1].As explained in the reference, two paths joining a given pair of points in a space E are homotopic if there exists a mapping F: I x I →E (I being the closed interval [0,1] ) which deforms one path continuously into the other. In practice, when two paths are homotopic and the mapping F is constructed, then the verification of all its required properties, with the possible exception of continuity, is trivial. The snag occurs when F is a combination of two or three functions on different subsets of I x I. Then the boundary lines between these subsets have to be given special consideration, and although the problems resulting are routine their disposal can involve some tedious calculation and repetition. In the development [l] of the fundamental group of a space, for example, this sort of situation comes up four or five times.
On an Extremal Problem in Fourier Series
Authors: Lorch Lee 
Published: December 2010

Let f(x) be a bounded odd function, - π < x < π, |f(X)| ≤ 1, with non-negative Fourier coefficients bk, k = 1,2, ….Otto Szász [l] proved anew the existence of a bounded set of numbers {βn}, n = 1,2,…, such thatwhere βn is the smallest constant satisfying the above inequality and added that 2/π ≤ βn ≤ 4/π. He pointed out [1, p. 170] that β1 = 4/π and raised the question of the value of βn for n > 1.
On Birkhoff's Problem 73 For Monoids
Authors: Brainerd Barron 
Published: December 2010

Birkhoff in [2] poses the following problem:“Problem 73. Find necessary and sufficient conditions in order that the correspondence between the congruence relations and the (neutral) ideals of a lattice be one-one”.This problem has been solved by Areškin [l] and Hashimoto [3]. Essentially the conditions reduce to the r e quirement that the lattice be a generalized Boolean algebra.
On an Observation of M. Riesz
Authors: Scherk P. 
Published: December 2010

On a recent visit to Toronto, Professor Riesz made an interesting remark on the invariance of a certain cross-ratio, I wish to present a simple proof of his result.Let x = ( x1, x2, x3, x4), … denote homogeneous coordinates in real projective three-space; x(t), … are differentiable curves in that space.
A Finite Packing Problem
Authors: Oler Norman 
Published: December 2010

The maximum density of packings of a given type into the whole of a Euclidean space is defined to be the limit of the maximum density of such packings into a cube as the edge of the cube goes to infinity.For E2 in particular, a number of well known results such as those due to A. Thue [1], L. Fejes-Toth [2], and C. A. Rogers [3] yield precise information about packings into the whole space. They are however of limited applicability to problems of finite packing in so-far as each requires some restriction upon the boundary of the configuration.
Sur les Anneaux Partiellement Ordonnés
Authors: Thierrin G. 
Published: December 2010

Un anneau partiellement ordonné A est un anneau sur lequel est définie une
relation d'ordre partiel telle que:1.a≥b entraîne a+c≥+c pour tout c∈A.2.a≥o et b≥o entraînent ab≥o.Si la relation d'ordre est une relation d1 ordre total, l'anneau A est dit
un anneau totalement ordonné.Il est bien connu (Théorème d'artin-Schreier [l]) que, pour qu'un corps
commutatif K puisse être totalement ordonné, il faut et il suffit que la
relation entraîne
a1=…=an=o. Ce théorème a été généralisé par T.
Szele [4] qui a montré que, pour qu'un corps quelconque K puisse être
totalement ordonné, il faut et il suffit que le demi-groupe additif et
multiplicatif S, engendré par les éléments de K qui sont des carrés non
nuls, ne contienne pas I'élément zéro de K. Ce résultat a été étendu au cas
d1 un anneau d'intégrité par R.E. Johnson [2] de la manière suivante.
Sur un Probléme de P. Scherk, Concernant la Somme des Carrés de
Deux Dérivées
Authors: Iosifescu Marius , Marcus Solomon 
Published: December 2010

P. Scherk a posé le problème suivant (Canadian Mathematical Bulletin, vol.4,
no. 3, 1961, p. 306, problème 49):Let x(t) and y(t) be two differentiable functions defined in some interval.
Does the function have the
Darboux property?La réponse est négative. En effet, Witold Wilkosz (Some properties of
derivative functions, Fundam. Math. vol.2, 1921, p. 145−154) a montré (p.
146−147 loc. cit.) que la fonction