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Item Details
| Title:
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P-ADIC AUTOMORPHIC FORMS ON SHIMURA VARIETIES
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| By: |
Haruzo Hida |
| Format: |
Paperback |
| List price:
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£119.99 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
1441919236 |
| ISBN 13: |
9781441919236 |
| Publisher: |
SPRINGER-VERLAG NEW YORK INC. |
| Pub. date: |
29 September, 2011 |
| Edition: |
Softcover reprint of the original 1st ed. 2004 |
| Series: |
Springer Monographs in Mathematics |
| Pages: |
390 |
| Synopsis: |
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. |
| Illustrations: |
biography |
| Publication: |
US |
| Imprint: |
Springer-Verlag New York Inc. |
| Returns: |
Returnable |
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