A First Course in Modular Forms (Graduate Texts in Mathematics) pdf epub mobi txt 電子書下載2025

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出版者:Springer

作者:Fred Diamond

出品人:

頁數:452

译者:

出版時間:2007-04-30

價格:USD 69.95

裝幀:Hardcover

isbn號碼:9780387232294

叢書系列:Graduate Texts in Mathematics

圖書標籤:

模形式
數學
modular_forms
數論
自守形式
橢圓麯綫
math
Number_Theory

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This book introduces the theory of modular forms with an eye toward the Modularity Theorem. All rational elliptic curves arise from modular forms. The topics covered include: elliptic curves as complex tori and as algebraic curves, modular curves as Riemann surfaces and as algebraic curves, Hecke operators and Atkin-Lehner theory, Hecke eigenforms and their arithmetic properties, the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms, elliptic and modular curves modulo p and the Eichler-Shimura Relation, the Galois representations associated to elliptic curves and to Hecke eigenforms. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory. A First Course in Modular Forms is written for beginning graduate students and advanced undergraduates. It does not require background in algebraic number theory or algebraic geometry, and it contains exercises throughout.</P>

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花瞭10分鍾速度翻完。內容主要是介紹moduilarity theorem：任何一個Elliptic curve E/Q, 均存在一個N 以及一個morphism F: X_0(N) ightarrow E, over Q 也就是說，Elliptic Curve實際上是由Hecke newform通過Eichler-Shimura理論得到。雖然描述瞭不同版本的modularity，但...

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