Arithmetic and Analytic Theories of Quadratic Forms and Clifford Groups - Couverture souple

Shimura, Goro

Couverture souple

ISBN 10 : 1470415623 ISBN 13 : 9781470415624

Editeur : American Mathematical Society, 2014

Synopsis

The 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.

A propos du livre

À propos de l'auteur

Goro Shimura, Princeton University, NJ, USA.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2014
• Langue: anglais
• ISBN 10: 1470415623
• ISBN 13: 9781470415624
• Reliure: Broché
• Nombre de pages: 275
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible