F. Diamond, J. Shurman A First Course in Modular Forms Series: Graduate Texts in Mathematics, Vol. 228
▶ Explores many topics not covered in other texts on the subject ▶ The theorem is stated in various forms, and related to one another ▶ Requires no background in algebraic number theory or algebraic geometry
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,
2005, XVI, 450 p. 57 illus. • modular curves as Riemann surfaces and as algebraic curves,
• Hecke operators and Atkin–Lehner theory, Printed book • Hecke eigenforms and their arithmetic properties, Hardcover
▶ 59,99 € | £53.99 | $79.99 • the Jacobians of modular curves and the Abelian varieties associated to Hecke ▶ *64,19 € (D) | 65,99 € (A) | CHF 67.07 eigenforms,
eBook • elliptic and modular curves modulo p and the Eichler–Shimura Relation,
Available from your bookstore or • the Galois representations associated to elliptic curves and to Hecke eigenforms. ▶ springer.com/shop
As it presents these ideas, the book states the Modularity Theorem in various forms, MyCopy 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 Printed eBook for just undergraduates. It does not require background in algebraic number theory or algebraic ▶ € | $ 24.99 geometry, and it contains exercises throughout. Fred Diamond received his Ph.D from ▶ springer.com/mycopy 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.
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