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Title:P-Adic Automorphic Forms on Shimura Varieties
Format Type:Ebook
Author:Haruzo Hida
Publisher:Springer
ISBN:0387207112
ISBN 13:
Number of Pages:390
Category:Manga

P-Adic Automorphic Forms on Shimura Varieties by Haruzo Hida

PDF, EPUB, MOBI, TXT, DOC P-Adic Automorphic Forms on Shimura Varieties In the early years of the s while I was visiting the Institute for Ad vanced Study lAS at Princeton as a postdoctoral member I got a fascinating view studying congruence modulo a prime among elliptic modular forms that an automorphic L function of a given algebraic group G should have a canon ical p adic counterpart of several variables I immediately decided to find out the reason behind this phenomenon and to develop the theory of ordinary p adic automorphic forms allocating to years from that point putting off the intended arithmetic study of Shimura varieties via L functions and Eisenstein series for which I visited lAS Although it took more than years we now know at least conjecturally the exact number of variables for a given G and it has been shown that this is a universal phenomenon valid for holomorphic automorphic forms on Shimura varieties and also for more general nonholomorphic cohomological automorphic forms on automorphic manifolds in a markedly different way When I was asked to give a series of lectures in the Automorphic Semester in the year at the Emile Borel Center Centre Emile Borel at the Poincare Institute in Paris I chose to give an exposition of the theory of p adic ordinary families of such automorphic forms p adic analytically de pending on their weights and this book is the outgrowth of the lectures given there

Modular Forms and Galois Cohomology, Elliptic Curves and Arithmetic Invariants, Modular Forms and Galois Cohomology, Elementary Theory of L-Functions and Eisenstein Series, Hilbert Modular Forms and Iwasawa Theory, p-Adic Automorphic Forms on Shimura Varieties (Springer Monographs in Mathematics), Geometric Modular Forms and Elliptic Curves, Contributions to Automorphic Forms, Geometry, and Number Theory: A Volume in Honor of Joseph Shalika, P-Adic Automorphic Forms on Shimura Varieties, Geometric Modular Forms and Elliptic Cur