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Book review

Author(s) David, Sinnou (ed.)
Title Séminaire de Théorie des Nombres, Paris 1990-1991
Publisher Birkhäuser-Verlag
Year of publication 1993
Reviewed by Andrei Marcus

This book is the twelfth volume of the series dedicated to the Séminaire de Théorie des Nombres de Paris. The content is based on the written versions of the lectures given by several experts in Number Theory at the Séminaire in 1990-1991. The volume includes both research papers and original synthesis of recent results.

Let me ennumerate the authors and their papers: S. Bosch, Riemann's Period Relations; J. Brüdern, A Note on cubic exponential sums; H. Cohen, F. Diaz, Y. Diaz and M. Olivier, Calculs de nombres de classes et de régulateurs de corps quadratiques en temps sous-exponentiel; J.C. Douai, Monodromie et Arithmétique des Surfaces; E. Fouvry, Sur le comportement en moyenne du rang des courbes y^2 = x^3 + k; G. Henniart, Correspondance de Jacquet-Langlands explicite I: le case Modéré de degré premier; A. Ivic, La valeur moyenne de la fonction zeta de Riemann; J. Nekovar, On p-adic heights pairing; B. Perrin-Riou, Théorie d'Iwasawa et hauteurs p-adiques; A. Silverberg, Galois representations attached to point on Shimura varieties; A.J. van der Poorten, Power series representing algebraic functions; Y.G. Zarhin, Abelian varieties of K3 type.

These papers cover a wide range of modern trends in Number Theory and should form a starting point for further research. Therefore, the volume will be a very good investment for specialists, and also libraries are warmly recommended to purchase it.