This is the sixth annual volume of papers based on the outstanding lectures given at the Séminaire de Théorie des Nombres de Paris. The results presented in 1985-86 by an international group of mathematicians reflect the most recent work in many areas of number theory.

Computing Stable Reductions.-Résultats Rédents Liés au Théorèe d¿irréductibilité de Hibert.-Elliptic Curves and Solutions of A-B=c.-Poincaré Series.-Kloosterman Sums, Trace Formulas, and Automorphic Forms for GL(n).-Some Recent Results on Complex Powers and Zeta Distributions.-Survey of the Proof of the Tate Conjectures for Hilbert-Blumenthal Surfaces.-Sur la Remification des Extensions Infinies de Corps Locaux.-Une nouvelle demonstration du theorem d¿isogénie, d¿après D.V. et G.V. Choodnovsky.-On Quadratic Gauss Sums over Local Fields.-Points entiers de variétés arithmétiques.-Approximants de Padé et mesures effectives d¿irrationalité.-Descents on Elliptic Curves with Complex Multiplication.-On the Arthmetic of Conic Bundle Surfaces.-Modular Forms on Noncongruence Subgroups.-Liste des Conférenciers.-Erratum à l¿article 'Multiplication Complexe dans les Pinceaux de variétés abéliennes' par Yves André.