høj kvalitet produkt Padic Automorphic Forms On Shimura Varie by Hida Haruzo U0JBVbf4

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In the early years of the 1980s 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 10 to 15 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 15 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 2000 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.