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040			_aIIITD
082			_a516.35 _bKOB-I
100			_aKoblitz, Neal
245			_aIntroduction to elliptic curves and modular forms _cby Neal Koblitz
250			_a2nd ed.
260			_bSpringer, _aNew York : _c©1993
300			_ax, 248 p. : _bill. ; _c24 cm.
490			_aGraduate texts in mathematics ; _v97
504			_aThis book includes bibliographical references and an index.
505			_tChapter I. From Congruent Numbers to Elliptic Curves _t1. Congruent numbers 2. A certain cubic equation 3. Elliptic curves 4. Doubly periodic functions 5. The field of elliptic functions 6. Elliptic curves in Weierstrass form 7. The addition law 8. Points of finite order 9. Points over finite fields, and the congruent number problem _tChapter II. The Hasse-Weil L-Function of an Elliptic Curve _t1. The congruence zeta-function 2. The zeta-function of E[subscript n] 3. Varying the prime p 4. The prototype: the Riemann zeta-function 5. The Hasse-Weil L-function and its functional equation 6. The critical value _tChapter III. Modular forms _t1. SL[subscript 2](Z) and its congruence subgroups 2. Modular forms for SL[subscript 2](Z) 3. Modular forms for congruence subgroups 4. Transformation formula for the theta-function 5. The modular interpretation and Hecke operators _tChapter IV. Modular Forms of Half Integer Weight _t1. Definitions and examples 2. Eisenstein series of half integer weight for [actual symbol not reproducible](4) 3. Hecke operators on forms of half integer weight 4. The theorems of Shimura, Waldspurger, Tunnell, and the congruent number problem
650			_aNumber theory
650			_aCurves, Elliptic
650			_aForms, Modular
650			_aGeometry, Algebraic
650			_aMathematics
942			_2ddc _cBK
999			_c171833 _d171833