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商品詳細
A First Course in Modular Forms. 1st ed. Softcover of orig. ed. 2005.
・ISBN 978-1-4419-2005-8 paper EUR 64.99
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お気に入り
★★★
| 著者・編者 | Diamond, Fred / Shurman, Jerry, |
|---|---|
| シリーズ | Graduate Texts in Mathematics |
| 出版社 | (Springer-Verlag New York Inc., US) |
| 出版年月 | 2010 |
| ページ数 | 450 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-19095＞ |
解説
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 received his Ph.D from Princeton University in 1988 under the direction of Goro Shimura and now teaches at Reed College.
*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 received his Ph.D from Princeton University in 1988 under the direction of Goro Shimura and now teaches at Reed College.