Elliptic Functions
Elliptic functions parametrize elliptic curves, and the intermingling of the analytic and algebraic-arithmetic theory has been at the center of mathematics since the early part of the nineteenth century. The book is divided into four parts. In the first, Lang presents the general analytic theory sta...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
1987, 1987
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| Edition: | 2nd ed. 1987 |
| Series: | Graduate Texts in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- One General Theory
- 1 Elliptic Functions
- 2 Homomorphisms
- 3 The Modular Function
- 4 Fourier Expansions
- 5 The Modular Equation
- 6 Higher Levels
- 7 Automorphisms of the Modular Function Field
- Two Complex Multiplication Elliptic Curves With Singular Invariants
- 8 Results from Algebraic Number Theory
- 9 Reduction of Elliptic Curves
- 10 Complex Multiplication
- 11 Shimura’s Reciprocity Law
- 12 The Function ?(??)/?(?)
- 13 The ?-adic and p-adic Representations of Deuring
- 14 Ihara’s Theory
- Three Elliptic Curves with Non-Integral Invariant
- 15 The Tate Parametrization
- 16 The Isogeny Theorems
- 17 Division Points Over Number Fields
- Four Theta Functions and Kronecker Limit Formula
- 18 Product Expansions
- 19 The Siegel Functions and Klein Forms
- 20 The Kronecker Limit Formulas
- 21 The First Limit Formula and L-series
- 22 The Second Limit Formula and L-series
- Appendix 1 Algebraic Formulas in Arbitrary Characteristic
- By J. Tate
- 1 Generalized Weierstrass Form
- 2 Canonical Forms
- Appendix 2 The Trace of Frobenius and the Differential of First Kind
- 1 The Trace of Frobenius
- 2 Duality
- 3 The Tate Trace
- 4 The Cartier Operator
- 5 The Hasse Invariant