Arithmetic and analytic theories of quadratic forms and Clifford groups
著者
書誌事項
Arithmetic and analytic theories of quadratic forms and Clifford groups
（Mathematical surveys and monographs, v. 109）
American Mathematical Society, c2004
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注記
Includes bibliographical references (p. 272-273) and index
内容説明・目次
内容説明
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'.
目次
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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