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Full Description
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.
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.
