A First Course in Modular Forms
1st ed. 2005. Corr. 3nd printing 2007
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First Course in Modular Forms by Fred Diamond
Book DescriptionThis book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers 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. 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. The authors assume no background in algebraic number theory and algebraic geometry. Exercises are included.
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Book DetailsISBN: 9780387232294
(234mm x 156mm x 25mm)
Imprint: Springer-Verlag New York Inc.
Publisher: Springer-Verlag New York Inc.
Publish Date: 30-Apr-2007
Country of Publication: United States
Books By Author Fred Diamond
Automorphic Forms and Galois Representations: Volume 1, Paperback (October 2014)» View all books by Fred Diamond
Part one of a two-volume collection exploring recent developments in number theory related to automorphic forms and Galois representations.
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