Topics in Number Theory: In Honor of B. Gordon and S. Chowla / Edition 1

by Scott D. Ahlgren, George E. Andrews, Ken Ono

Overview

From July 31 through August 3,1997, the Pennsylvania State University hosted the Topics in Number Theory Conference. The conference was organized by Ken Ono and myself. By writing the preface, I am afforded the opportunity to express my gratitude to Ken for beng the inspiring and driving force behind the whole conference. Without his energy, enthusiasm and skill the entire event would never have occurred. We are extremely grateful to the sponsors of the conference: The National Sci­ ence Foundation, The Penn State Conference Center and the Penn State Depart­ ment of Mathematics. The object in this conference was to provide a variety of presentations giving a current picture of recent, significant work in number theory. There were eight plenary lectures: H. Darmon (McGill University), "Non-vanishing of L-functions and their derivatives modulo p. " A. Granville (University of Georgia), "Mean values of multiplicative functions. " C. Pomerance (University of Georgia), "Recent results in primality testing. " C. Skinner (Princeton University), "Deformations of Galois representations. " R. Stanley (Massachusetts Institute of Technology), "Some interesting hyperplane arrangements. " F. Rodriguez Villegas (Princeton University), "Modular Mahler measures. " T. Wooley (University of Michigan), "Diophantine problems in many variables: The role of additive number theory. " D. Zeilberger (Temple University), "Reverse engineering in combinatorics and number theory. " The papers in this volume provide an accurate picture of many of the topics presented at the conference including contributions from four of the plenary lectures.

Product Details

ISBN-13:	9780792355830
Publisher:	Springer US
Publication date:	03/31/1999
Series:	Mathematics and Its Applications , #467
Edition description:	1999
Pages:	264
Product dimensions:	6.30(w) x 9.45(h) x 0.03(d)

Table of Contents

Motivating the multiplicative spectrum.- Modular Mahler measures I.- Diophantine problems in many variables: The role of additive number theory.- Equations F(x, y,—x) = 0.- A fundamental invariant in the theory of partitions.- Congruence properties of values of L-functions and applications.- On Tschirnhaus transformations.- Hecke operators and the nonvanishing of L-functions.- A new minor-arcs estimate for number fields.- Modular functions, Maple and Andrews’ tenth problem.- Hecke characters and formal group characters.- On certain Gauss periods with common decomposition field.- Theorems and conjectures involving rook polynomials with only real zeros.- An example of an elliptic curve with a positive density of prime quadratic twists which have rank zero.- Exponents of class groups of quadratic fields.- A local-global principle for densities.- Divisibility of the specialization map for twists of abelian varieties.

Editorial Reviews

The proceedings of the August 1997 conference contains 17 research papers reporting recent, significant work in many areas of number theory. The contributions from three of the plenary speakers are titled: motivating the multiplicative spectrum, modular Mahler measures, and the role of additive number theory in diophantine problems in many variable. Other topics are a fundamental invariant in the theory of partitions, a new minor-arcs estimate for number fields, Hecke characters and formal group characters, theorems and conjectures involving rook polynomials with only real zeros, and the divisibility of the specialization map for twists of abelian varieties. No index. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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