000			01496nam a2200277Ia 4500
003			OSt
005			20240131154726.0
008			231229s9999 xx 000 0 und d
020			_a9781441920058
040			_cIISER BPR
041			_aEng
082			_a512.73 _bDIA _223rd
100			_aDiamond, Fred
245		2	_aFirst course in modular forms
250			_a1st ed.
260			_aNew York: _bSpringer Science, _cc2005.
300			_axvi, 450p. : _bill (pbk). ; _c22cm.
440			_aGraduate texts in mathematics ; _vVol. 228
520			_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 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. Also includes List of symbols, index and references.
651			_aMathematics
651			_aModular Forms
700			_aShurman, Jerry
942			_cBK _2ddc
947			_a5700.721330999999
948			_a0.22
999			_c3201 _d3201