000			01218nam a22001817a 4500
008			211124b2005 |||||||| |||| 00| 0 eng d
020			_a9780387232294
082			_a512.7 DIA-F
100			_aDiamond, Fred
245			_aA first course in modular forms / _cFred Diamond and Jerry Shurman
260			_aNew York _bSpringer _c2005
300			_a450 p.
365			_aEU _b59.99.
500			_aThis 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 with 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.
650			_aForms, Modular
650			_aNumber theory
650			_aGeometry, Algebraic
999			_c71363 _d71363