Haruzo Hida

Gebundenes Buch

P-Adic Automorphic Forms on Shimura Varieties

Beschreibung

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 (ina 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.

Autor

Haruzo Hida, University of California, Los Angeles, CA, USA

Produktdetails

• Springer Monographs in Mathematics
• Verlag: Springer / Springer New York / Springer, Berlin
• Artikelnr. des Verlages: 978-0-387-20711-7
• 2004 edition
• Seitenzahl: 390
• Erscheinungstermin: 10. Mai 2004
• Englisch
• Abmessung: 246mm x 162mm x 24mm
• Gewicht: 795g
• ISBN-13: 9780387207117
• ISBN-10: 0387207112
• Artikelnr.: 12633034