| 期刊全称 | A First Course in Modular Forms | | 影响因子2023 | Fred Diamond,Jerry Shurman | | 视频video | | | 发行地址 | Covers many topics not covered in other texts on elliptic curves.Includes supplementary material: | | 学科分类 | Graduate Texts in Mathematics | | 图书封面 |  | | 影响因子 | 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..Fred Diamond received his Ph.D from Princeton University in 1988 under the direction of Andrew Wiles and now teaches at King‘s College London. Jerry Shurman receive | | Pindex | Textbook 2005 |
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发表于 2025-3-21 19:41:23
