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First Course in Modular Forms

Name: First Course in Modular Forms
Brand: Springer-Verlag New York Inc.
SKU: 01381046
Price: 23786 HUF
Availability: InStock
Author: Fred Diamond
ISBN: 9780387232294

Fred Diamond

Jerry Shurman

Language

English

Book Hardback

Libristo code: 01381046

Publishers Springer-Verlag New York Inc., September 2016

This book introduces the theory of modular forms with an eye toward the Modularity Theorem. All rati... Full description

Libristo code: 01381046

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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.