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OverviewThe two main themes of the book are (1) quadratic Diophantine equations; (2) Euler products and Eisenstein series on orthogonal groups and Clifford groups. Whereas the latest chapters of the book contain new results, a substantial portion of it is devoted to expository material related to these themes, such as Witt's theorem and the Hasse principle on quadratic forms, algebraic theory of Clifford algebras, spin groups, and spin representations. The starting point of the first main 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. A generalization of this fact for arbitrary quadratic forms over algebraic number fields, as well as various applications are presented. As for the second theme, the existence of the meromorphic continuation of an Euler product associated with a Hecke eigenform on a Clifford or an orthogonal group is proved. The same is done for an Eisenstein series on such a group. The book is practically self-contained, except that familiarity with algebraic number theory is assumed and several standard facts are stated without detailed proof, but with precise references. Full Product DetailsAuthor: Goro ShimuraPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: 109 Weight: 0.498kg ISBN: 9781470415624ISBN 10: 1470415623 Pages: 275 Publication Date: 31 May 2014 Audience: Adult education , Further / Higher Education Format: Paperback Publisher's Status: Active Availability: Temporarily unavailable  The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you. Table of ContentsIntroduction 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 IndexReviewsAuthor InformationGoro Shimura, Princeton University, NJ, USA. Tab Content 6Author Website:Countries AvailableAll regions |
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