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A First Course in Modular Forms (Electronic book text)
A First Course in Modular Forms (Electronic book text): Fred Diamond, Jerry Shurman
A First Course in Modular Forms (Electronic book text): Fred Diamond, Jerry Shurman

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A First Course in Modular Forms (Electronic book text)

Fred Diamond, Jerry Shurman

Series: Graduate Texts in Mathematics, 228

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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.

General

Imprint: Springer Science+Business Media
Country of origin: United States
Series: Graduate Texts in Mathematics, 228
Release date: 2005
Authors: Fred Diamond • Jerry Shurman
Format: Electronic book text
Pages: 447
ISBN-13: 978-0-387-27226-9
Barcode: 9780387272269
Categories: Promotions
Books > Science & Mathematics > Mathematics > Number theory
Books > Science & Mathematics > Mathematics > Number theory > General
Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
LSN: 0-387-27226-7

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