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Elliptic Functions

  • Textbook
  • © 1985

Overview

Authors:
  1. Komaravolu Chandrasekharan

    1. Eidgenössische Technische Hochschule Zürich, Zürich, Switzerland

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Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 281)

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-XI
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  2. Periods of meromorphic functions

    • Komaravolu Chandrasekharan
    Pages 1-20

  3. General properties of elliptic functions

    • Komaravolu Chandrasekharan
    Pages 21-25

  4. Weierstrass’s elliptic function ℘(z)

    • Komaravolu Chandrasekharan
    Pages 26-47

  5. The zeta-function and the sigma-function of Weierstrass

    • Komaravolu Chandrasekharan
    Pages 48-57

  6. The theta-functions

    • Komaravolu Chandrasekharan
    Pages 58-80

  7. The modular function J(τ)

    • Komaravolu Chandrasekharan
    Pages 81-98

  8. The Jacobian elliptic functions and the modular functionλ(τ)

    • Komaravolu Chandrasekharan
    Pages 99-121

  9. Dedekind’s η-function and Euler’s theorem on pentagonal numbers

    • Komaravolu Chandrasekharan
    Pages 122-140

  10. The law of quadratic reciprocity

    • Komaravolu Chandrasekharan
    Pages 141-154

  11. The representation of a number as a sum of four squares

    • Komaravolu Chandrasekharan
    Pages 155-169

  12. The representation of a number by a quadratic form

    • Komaravolu Chandrasekharan
    Pages 170-184

  13. Back Matter

    Pages 185-192
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Keywords

About this book

This book has grown out of a course of lectures on elliptic functions, given in German, at the Swiss Federal Institute of Technology, Zurich, during the summer semester of 1982. Its aim is to give some idea of the theory of elliptic functions, and of its close connexion with theta-functions and modular functions, and to show how it provides an analytic approach to the solution of some classical problems in the theory of numbers. It comprises eleven chapters. The first seven are function-theoretic, and the next four concern arithmetical applications. There are Notes at the end of every chapter, which contain references to the literature, comments on the text, and on the ramifications, old and new, of the problems dealt with, some of them extending into cognate fields. The treatment is self-contained, and makes no special demand on the reader's knowledge beyond the elements of complex analysis in one variable, and of group theory.

Reviews

"...In the breadth, depth and inevitability of treatment of this beautiful material, the author has made a contribution to the mathematical community consistent with the distinction of his career. That he has succeeded in compressing this treatment into a succinct monograph of fewer than 190 pages is a testament to his taste, discipline and powers of exposition."-- MATHEMATICAL REVIEWS

Authors and Affiliations

  • Eidgenössische Technische Hochschule Zürich, Zürich, Switzerland

    Komaravolu Chandrasekharan

Bibliographic Information

  • Book Title: Elliptic Functions

  • Authors: Komaravolu Chandrasekharan

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-642-52244-4

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1985

  • Hardcover ISBN: 978-3-540-15295-8Published: 01 September 1985

  • Softcover ISBN: 978-3-642-52246-8Published: 28 June 2012

  • eBook ISBN: 978-3-642-52244-4Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: XI, 192

  • Topics: Number Theory, Special Functions

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