This 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.
General
| Imprint: |
Springer-Verlag New York
|
| Country of origin: |
United States |
| Series: |
Graduate Texts in Mathematics, 228 |
| Release date: |
September 2016 |
| First published: |
2005 |
| Authors: |
Fred Diamond
• Jerry Shurman
|
| Dimensions: |
235 x 155 x 33mm (L x W x T) |
| Format: |
Hardcover
|
| Pages: |
450 |
| Edition: |
1st ed. 2005, Corr. 4th printing 2016 |
| ISBN-13: |
978-0-387-23229-4 |
| Categories: |
Books >
Science & Mathematics >
Mathematics >
Number theory >
General
Promotions
|
| LSN: |
0-387-23229-X |
| Barcode: |
9780387232294 |
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