Number Theory for the Millennium II

Bruce Berndt

• Publisher: A K Peters/CRC Press
• Year: 2024
• ISBN:
  9780429605888
• Edition: 1
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

Building on the tradition of an outstanding series of conferences at the University of Illinois at Urbana-Champaign, the organizers attracted an international group of scholars to open the new Millennium with a conference that reviewed the current state of number theory research and pointed to future directions in the field. The conference was the largest general number theory conference in recent history, featuring a total of 159 talks, with the plenary lectures given by George Andrews, Jean Bourgain, Kevin Ford, Ron Graham, Andrew Granville, Roger Heath-Brown, Christopher Hooley, Winnie Li, Kumar Murty, Mel Nathanson, Ken Ono, Carl Pomerance, Bjorn Poonen, Wolfgang Schmidt, Chris Skinner, K. Soundararajan, Robert Tijdeman, Robert Vaughan, and Hugh Williams. The Proceedings Volumes of the conference review some of the major number theory achievements of this century and to chart some of the directions in which the subject will be heading during the new century. These volumes will serve as a useful reference to researchers in the area and an introduction to topics of current interest in number theory for a general audience in mathematics.

Table of contents

• Cover Page
• Half Title page
• Title Page
• Copyright Page
• Contents of Volume 1
• Contents of Volume 2
• Contents of Volume 3
• Preface
• List of Contributors
• Coverings of the Integers Associated with an Irreducibility Theorem of A. Schinzel
• Zero-free Regions for the Riemann Zeta Function
• Asymptotic Lower Bounds and Formulas for Diophantine Inequalities
• Shifted and Shiftless Partition Identities
• Deformations of Pseudorepresentations Coming from Reducible Representations
• The Sum of Multiplicative Functions Arising in Selberg's Sieve
• Siegel Modular Forms and Hecke Operators in Degree 2
• One Hundred Years of Normal Numbers
• A Reciprocity Relation Between Some
• On the Spectrum of the Transfer Operator for Continued Fractions with Restricted Partial Quotients
• On Theorems of Barban-Davenport-Halberstam Type
• Elementary Evaluation of Certain Convolution Sums Involving Divisor Functions
• Integer Points, Exponential Sums and the Riemann Zeta Function
• Euler Products and Abstract Trace Formulas
• On a Binary Diophantine Inequality Involving Prime Powers
• Recent Developments in Automorphic Forms and Applications
• Convergence of Corresponding Continued Fractions
• Reducible Arithmetic Functions, Asymptotic Mean Behavior, and Polylogarithms
• On the Probability of Combinatorial Structures Without Some Components
• Asymmetries in the Shanks—Rényi Prime Number Race
• On the Analytic Continuation of Various Multiple Zeta-Functions
• Three-Term Relations for Some Analogues of the Dedekind Sum