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.
Contents of Volume III: Some remarks on primarily testing based on Lucas Functions; Splitting primes in Infinite Extensions; The ABC conjecture and prime divisors of the Lucas and Lehmer Sequences; On the parity of generalised partition functions; Quadratic twists of modular forms and elliptic curves; Identities from Holomorphic projection of modular forms; Iterative methods for pairs of additive diophantine equations; Quelques remarques sur la theore d'Iwasawa des Courbes Elliptiques; Computing Rational Points on curves; Norms of products and factors of polynomials; G.H Hatdy as I knew him; Discriminants of some painleve polynomials; Identities between Malher measures' Normal integral bases, swam modules and p-Adic L-functions; Discriminants and divisibility for Chebyseh-like polynomimals; Remarks on Adelic geometry of numbers; Some applications of Diophantine approximation; On the solutions of a family of sextic thue equations; Waring's problem: a survey; Chernoff type bounds for sums of dependent random variables and applications in additive number theory; prime divisors of the Bernoulli and Euler numbers; An improved method for solving the family of Thue equations; Constructing Hyperelliptic curves using complex multiplication; Solving the Pell equation; A central limit theorem for the Number of distinct degrees of prime factors in additive arithmetical semigroups.
"The conference was one of the most important international meetings devoted to number theory . . . . Consequently the interested reader finds here not only surveys on the most important contributions to number theory and its applications, but also surveys on methods and techniques used in this important branch of mathematics." -EMS Newsletter December 2004