| 期刊全称 | Arithmetic of Quadratic Forms | | 影响因子2023 | Goro Shimura | | 视频video | | | 发行地址 | Discusses algebraic number theory and the theory of semisimple algebras.Discusses classification of quadratic forms over the ring of algebraic integers.Discusses local class field theory.Presents a ne | | 学科分类 | Springer Monographs in Mathematics | | 图书封面 |  | | 影响因子 | This book can be divided into two parts. The ?rst part is preliminary and consists of algebraic number theory and the theory of semisimple algebras. The raison d’ˆ etre of the book is in the second part, and so let us ?rst explain the contents of the second part. There are two principal topics: (A) Classi?cation of quadratic forms; (B) Quadratic Diophantine equations. Topic (A) can be further divided into two types of theories: (a1) Classi?cation over an algebraic number ?eld; (a2) Classi?cation over the ring of algebraic integers. To classify a quadratic form ? over an algebraic number ?eld F, almost all previous authors followed the methods of Helmut Hasse. Namely, one ?rst takes ? in the diagonal form and associates an invariant to it at each prime spot of F, using the diagonal entries. A superior method was introduced by Martin Eichler in 1952, but strangely it was almost completely ignored, until I resurrected it in one of my recent papers. We associate an invariant to ? at each prime spot, which is the same as Eichler’s, but we de?ne it in a di?erent and more direct way, using Cli?ord algebras. In Sections 27 and 28 we give an exposition of this theory. At some point we need | | Pindex | Book 2010 |
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发表于 2025-3-21 19:55:56
