Download Haruzo Hida : P-Adic Automorphic Forms on Shimura Varieties books

P-Adic Automorphic Forms on Shimura Varieties Haruzo Hida - (Rating: 2 - 0 votes)

P-Adic Automorphic Forms on Shimura Varieties

P-Adic Automorphic Forms on Shimura Varieties - Read Online or Download P-Adic Automorphic Forms on Shimura Varieties by Haruzo Hida Book For Free. Available forma: PDF, TXT , ePub , PDB , RTF, Audio Books - 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."

This book covers the following three topics in a manner accessible to graduate students who have an understanding of algebraic number theory and scheme, Cite this chapter as: Hida H. (2004) Ordinary p-Adic Automorphic Forms. In: p-Adic Automorphic Forms on Shimura Varieties. Springer Monographs in Mathematics., Develops analytic, p-adic and geometric perspectives on families of automorphic forms in relation to the trace formula; Focuses on recent developments and conjectures ..., Derivative at s = 1 of the p-adic L-function of the symmetric square of a Hilbert modular form, In mathematics, the Langlands program is a web of far-reaching and influential conjectures that relate Galois groups in algebraic number theory to automorphic forms ..., Compiled by Keith Matthews as part of the Number Theory Web., Various Number Theorists' Home Pages/Departmental listings Complete listing [ A | B | C | D | E | F | G | :q! :q! A HREF="./list.html#H">H | I | J | K | L | M], Number theory and representation theory seminar Analytic number theory, algebraic number theory, arithmetic geometry, automorphic forms, and even some things not ..., () 2017, , 8/28-9/13031002 epub books 3031000 epub books