Diamond, Fred. <br/><br/>
A First Course in Modular Forms  [electronic resource] / 
by Fred Diamond, Jerry Shurman. 
 - XVI, 436 p. 29 illus.  online resource. 
 - Graduate Texts in Mathematics,  228  0072-5285 ; .
 - Graduate Texts in Mathematics,  228 .
<br/><br/>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. 
<br/><br/>ZDB-2-SMA 
<br/><br/> 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~ 
<br/><br/><label>ISBN: </label>9780387272269 
<br/><br/><label>Standard No.: </label>10.1007/b138781  doi 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Mathematics.<br/>Geometry, algebraic.<br/>Number theory.<br/>Mathematics.<br/>Number Theory.<br/>Algebraic Geometry.
<br/><br/><label>LC Class. No.: </label>QA241-247.5 
<br/><br/><label>Dewey Class. No.: </label>512.7