TY  - BOOK
AU  - 
AU  - 
ED  - SpringerLink (Online service)
TI  - A First Course in Modular Forms
T2  - Graduate Texts in Mathematics,
SN  - 9780387272269
AV  - QA241-247.5 
U1  - 512.7 23
PY  - 2005///
CY  - New York, NY
PB  - Springer New York
KW  - Mathematics
KW  - Geometry, algebraic
KW  - Number theory
KW  - Number Theory
KW  - Algebraic Geometry
N1  - Modular Forms, Elliptic Curves, and Modular Curves -- Modular Curves as Riemann Surfaces -- Dimension Formulas -- Eisenstein Series -- Hecke Operators -- Jacobians and Abelian Varieties -- Modular Curves as Algebraic Curves -- The Eichler-Shimura Relation and L-functions -- Galois Representations; ZDB-2-SMA
N2  - 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~
UR  - http://dx.doi.org/10.1007/b138781
ER  -