springer.com Mathematics : Number Theory Diamond, Fred, Shurman, Jerry A First Course in Modular Forms Covers many topics not covered in other texts on elliptic curves 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 Springer written for beginning graduate students and advanced undergraduates. It does not require 2005, XVI, 450 p. 57 illus. background in algebraic number theory or algebraic geometry, and it contains exercises 1st throughout. Fred Diamond received his Ph.D from Princeton University in 1988 under the edition 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. Printed book Hardcover Order online at springer.com/booksellers Springer Nature Customer Service Center LLC Printed book 233 Spring Street Hardcover New York, NY 10013 ISBN 978-0-387-23229-4 USA $ 79,99 T: +1-800-SPRINGER NATURE Available (777-4643) or 212-460-1500 Discount group [email protected] Professional Books (2) Product category Graduate/advanced undergraduate textbook Series Graduate Texts in Mathematics Other renditions Softcover ISBN 978-1-4419-2005-8 Prices and other details are subject to change without notice. All errors and omissions excepted. Americas: Tax will be added where applicable. Canadian residents please add PST, QST or GST. Please add $5.00 for shipping one book and $ 1.00 for each additional book. Outside the US and Canada add $ 10.00 for first book, $5.00 for each additional book. If an order cannot be fulfilled within 90 days, payment will be refunded upon request. Prices are payable in US currency or its equivalent. ISBN 978-0-387-23229-4 / BIC: PBH / SPRINGER NATURE: SCM25001 Part of .