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Ramanujan’s Notebooks

Part III

  • Book
  • © 1991

Overview

Authors:
  1. Bruce C. Berndt

    1. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, USA

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About this book

During the time period between 1903 and 1914, Ramanujan worked in almost complete isolation in India. Throughout these years, he recorded his mathematical results without proofs in notebooks. Upon Ramanujan's death in 1920, G.H. Hardy strongly urged that Ramanujan's notebooks be published and edited. The English mathematicians G.N. Watson and B.M. Wilson began this task in 1929, but although they devoted nearly ten years to the project, the work was never completed. In 1957, the Tata Institute of Fundamental Research in Bombay published a photostat edition of the notebooks, but no editing was undertaken. In 1977, Berndt began the tasks of editing Ramanujan's notebooks. Proofs are provided to theorems not yet proven in previous literature, and many results are so startling and different that there are no results akin to them in the literature.

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Introduction

    • Bruce C. Berndt
    Pages 1-10

  3. q-Series and Theta-Functions

    • Bruce C. Berndt
    Pages 11-86

  4. Fundamental Properties of Elliptic Functions

    • Bruce C. Berndt
    Pages 87-142

  5. The Jacobian Elliptic Functions

    • Bruce C. Berndt
    Pages 143-219

  6. Modular Equations of Degrees 3, 5, and 7 and Associated Theta-Function Identities

    • Bruce C. Berndt
    Pages 220-324

  7. Modular Equations of Higher and Composite Degrees

    • Bruce C. Berndt
    Pages 325-453

  8. Eisenstein Series

    • Bruce C. Berndt
    Pages 454-488

  9. Back Matter

    Pages 489-510
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Authors and Affiliations

  • Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, USA

    Bruce C. Berndt

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Bibliographic Information

  • Book Title: Ramanujan’s Notebooks

  • Book Subtitle: Part III

  • Authors: Bruce C. Berndt

  • DOI: https://doi.org/10.1007/978-1-4612-0965-2

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1991

  • Hardcover ISBN: 978-0-387-97503-0Published: 23 July 1991

  • Softcover ISBN: 978-1-4612-6963-2Published: 30 September 2012

  • eBook ISBN: 978-1-4612-0965-2Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XIII, 510

  • Topics: Number Theory

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