Series: Graduate Texts in Mathematics, Vol. 228
Diamond, Fred, Shurman, Jerry
2005, XV, 436 p. 29 illus.
Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.
You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.
After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.
(net)
price for USA
ISBN 978-0-387-27226-9
digitally watermarked, no DRM
Included Format: PDF
download immediately after purchase
Hardcover version
You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.
Standard shipping is free of charge for individual customers.
(net)
price for USA
ISBN 978-0-387-23229-4
free shipping for individuals worldwide
usually dispatched within 3 to 5 business days
Softcover (also known as softback) version.
You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.
Standard shipping is free of charge for individual customers.
(net)
price for USA
ISBN 978-1-4419-2005-8
free shipping for individuals worldwide
usually dispatched within 3 to 5 business days
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.
Fred Diamond received his Ph.D from Princeton University in 1988 under the direction of Andrew Wiles and now teaches at Brandeis University. Jerry Shurman received his Ph.D from Princeton University in 1988 under the direction of Goro Shimura and now teaches at Reed College.
Content Level » Graduate
Keywords » Abelian variety - Dimension - Grad - algebraic curve - algebraic geometry - number theory
Related subjects » Algebra - Number Theory and Discrete Mathematics
Get alerted on new Springer publications in the subject area of Number Theory.