Introduction to elliptic curves and modular forms
Koblitz, Neal
Introduction to elliptic curves and modular forms by Neal Koblitz - 2nd ed. - New York : Springer, ©1993 - x, 248 p. : ill. ; 24 cm. - Graduate texts in mathematics ; 97 .
This book includes bibliographical references and an index.
Chapter I. From Congruent Numbers to Elliptic Curves 1. 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 Chapter II. The Hasse-Weil L-Function of an Elliptic Curve 1. 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 Chapter III. Modular forms 1. 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 Chapter IV. Modular Forms of Half Integer Weight 1. 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
9780387979663
Number theory
Curves, Elliptic
Forms, Modular
Geometry, Algebraic
Mathematics
516.35 / KOB-I
Introduction to elliptic curves and modular forms by Neal Koblitz - 2nd ed. - New York : Springer, ©1993 - x, 248 p. : ill. ; 24 cm. - Graduate texts in mathematics ; 97 .
This book includes bibliographical references and an index.
Chapter I. From Congruent Numbers to Elliptic Curves 1. 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 Chapter II. The Hasse-Weil L-Function of an Elliptic Curve 1. 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 Chapter III. Modular forms 1. 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 Chapter IV. Modular Forms of Half Integer Weight 1. 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
9780387979663
Number theory
Curves, Elliptic
Forms, Modular
Geometry, Algebraic
Mathematics
516.35 / KOB-I