Introduction to elliptic curves and modular forms

By:

Koblitz, Neal

Material type: Text

9780387979663

Subject(s):

DDC classification:

516.35 KOB-I

Contents:

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

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Holdings
Item type	Current library	Collection	Call number	Status	Date due	Barcode	Item holds
Books	IIITD Reference	Mathematics	REF 516.35 KOB-I (Browse shelf(Opens below))	Available		012411

Total holds: 0

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

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