Arithmetic and analytic theories of quadratic forms and Clifford groups
Author(s)
Bibliographic Information
Arithmetic and analytic theories of quadratic forms and Clifford groups
(Mathematical surveys and monographs, v. 109)
American Mathematical Society, c2004
Available at 59 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
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Note
Includes bibliographical references (p. 272-273) and index
Description and Table of Contents
Description
In this book, award-winning author Goro Shimura treats new areas and presents relevant expository material in a clear and readable style. Topics of this book include, Witt's theorem and the Hasse principle on quadratic forms, algebraic theory of Clifford algebras, spin groups, and spin representations. He also includes some basic results not readily found elsewhere. The two principle themes are: Quadratic Diophantine equations and Euler products and Eisenstein series on orthogonal groups and Clifford groups.The starting point of the first theme is the result of Gauss that the number of primitive representations of an integer as the sum of three squares is essentially the class number of primitive binary quadratic forms. Presented are a generalization of this fact for arbitrary quadratic forms over algebraic number fields and various applications. For the second theme, the author proves the existence of the meromorphic continuation of a Euler product associated with a Hecke eigenform on a Clifford or an orthogonal group. The same is done for an Eisenstein series on such a group. Beyond familiarity with algebraic number theory, the book is mostly self-contained. Several standard facts are stated with references for detailed proofs. Goro Shimura won the 1996 Steele Prize for Lifetime Achievement for 'his important and extensive work on arithmetical geometry and automorphic forms'.
Table of Contents
Introduction Algebraic theory of quadratic forms, Clifford algebras, and spin groups Quadratic forms, Clifford groups, and spin groups over a local or global field Quadratic diophantine equations Groups and symmetric spaces over R Euler products and Eisenstein series on orthogonal groups Euler products and Eisenstein series on Clifford groups Appendix References Frequently used symbols Index.
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