Number Theory

The 15 papers of this selection of contributions to the Journées Arithmétiques 1987 include both survey articles and original research papers and represent a cross-section of topics such as Abelian varieties, algebraic integers, arithmetic algebraic geometry, additive number theory, computational number theory, exponential sums, modular forms, transcendence and Diophantine approximation, uniform distribution.

Contenu

Applications of Cayley-Chow forms.- Partitions into parts which are unequal and large.- Links between solutions of A?B=C and elliptic curves.- Factorizations of algebraic integers.- Etude d'une famille modulaire de variétés abéliennes.- Weyl's inequality and hua's inequality.- Positive definite binary quadratic forms over k[X].- Mean value estimates for exponential sums.- Some results on diophantine approximation related to Dirichlet's Theorem.- On cliques of exceptional units and Lenstra's construction of Euclidean fields.- Sumsets containing k-free integers.- On the representation of 1 by binary cubic forms with positive discriminant.- A linear relation between theta series of degree and weight 2.- Integral points on curves and surfaces.- Weak uniform distribution of second-order linear recurring sequences.- Correspondance modulaire galois - quaternions pour un corps p-adique.