Number Theory for the Millennium III

M. A. Bennett, B.C Berndt, N. Boston, H. G. Diamond, A. J. Hildebrand, W. Philipp

• 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