Number Theory for the Millennium III

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; Discriminantsof 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.