A First Course in Modular Forms: 228 (Graduate Texts in Mathematics, 228) - Hardcover

Diamond, Fred; Shurman, Jerry

Hardcover

ISBN 10: 038723229X ISBN 13: 9780387232294

Publisher: Springer, 2005

Synopsis

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.

About this title

Review

"It has always been difficult to start learning about modular forms. ... we were still lacking a textbook that could be honestly described as both comprehensive and accessible. Diamond and Shurman s First Course is a largely successful attempt to provide just such a book. ... A First Course in Modular Forms is a success. ... a course taught from this text would be a very good way to lead students into the area. ... I expect that Diamond and Shurman s book would serve very well." --Fernando Q. Gouvêa, MathDL, February, 2007

"While there are many books on modular forms and elliptic curves, and some of them discuss the Eicheler-Shimura theory, most that describe it do not go deeply into the proofs. ... The book of Diamond and Shurman addresses this need. ... it is clearly directed to the serious student and it will unquestionably be a useful book even to experts. ... this is a very unique and valuable book, and one that I would recommend to anyone wishing to learn about modular forms ... ." --Daniel Bump, SIAM Review, Vol. 47 (4), 2005

About the Author

Fred Diamond teaches at Brandeis University.

Edition details

• Publisher: Springer
• Publication date: 2005
• ISBN 10: 038723229X
• ISBN 13: 9780387232294
• Binding: Hardcover
• Language: English
• Number of pages: 466