Skip to content

Your Cambridge account can now be used to log into other Cambridge products and services including Cambridge One, Cambridge LMS, Cambridge GO and Cambridge Dictionary Plus

Register Sign in Wishlist

Elliptic and Modular Functions from Gauss to Dedekind to Hecke

  • Date Published: April 2017
  • availability: In stock
  • format: Hardback
  • isbn: 9781107159389


Add to wishlist

Other available formats:

Looking for an inspection copy?

This title is not currently available for inspection. However, if you are interested in the title for your course we can consider offering an inspection copy. To register your interest please contact providing details of the course you are teaching.

Product filter button
About the Authors
  • This thorough work presents the fundamental results of modular function theory as developed during the nineteenth and early-twentieth centuries. It features beautiful formulas and derives them using skillful and ingenious manipulations, especially classical methods often overlooked today. Starting with the work of Gauss, Abel, and Jacobi, the book then discusses the attempt by Dedekind to construct a theory of modular functions independent of elliptic functions. The latter part of the book explains how Hurwitz completed this task and includes one of Hurwitz's landmark papers, translated by the author, and delves into the work of Ramanujan, Mordell, and Hecke. For graduate students and experts in modular forms, this book demonstrates the relevance of these original sources and thereby provides the reader with new insights into contemporary work in this area.

    • Features detailed analysis of lost or little known methods and techniques used by Gauss, Jacobi, Riemann, Dedekind, Hurwitz, and others
    • A translation of Hurwitz's 1904 paper, not easily available in English, is included as an appendix
    • Exercises at the end of each chapter allow readers to extend their grasp of the material
    Read more

    Reviews & endorsements

    'Finally, it needs to be stressed that Roy does much more than present these mathematical works as museum pieces. He takes pains to tie them in to modern work when reasonable and appropriate, and that of course just adds to the quality of his work. I am very excited to have a copy of this wonderful book in my possession.' Michael Berg, MAA Reviews

    'This book will be a valuable resource for understanding modular functions in their historical context, especially for readers not fluent in the languages of the original papers.' Paul M. Jenkins, Mathematical Reviews

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: April 2017
    • format: Hardback
    • isbn: 9781107159389
    • length: 488 pages
    • dimensions: 261 x 182 x 31 mm
    • weight: 1.02kg
    • contains: 13 b/w illus.
    • availability: In stock
  • Table of Contents

    1. The basic modular forms
    2. Gauss's contributions to modular forms
    3. Abel and Jacobi on elliptic functions
    4. Eisenstein and Hurwitz
    5. Hermite's transformation of theta functions
    6. Complex variables and elliptic functions
    7. Hypergeometric functions
    8. Dedekind's paper on modular functions
    9. The n function and Dedekind sums
    10. Modular forms and invariant theory
    11. The modular and multiplier equations
    12. The theory of modular forms as reworked by Hurwitz
    13. Ramanujan's Euler products and modular forms
    14. Dirichlet series and modular forms
    15. Sums of squares
    16. The Hecke operators.

  • Author

    Ranjan Roy, Beloit College, Wisconsin
    Ranjan Roy is the Huffer Professor of Mathematics and Astronomy at Beloit College, Wisconsin, and has published papers in differential equations, fluid mechanics, complex analysis, and the development of mathematics. He received the Allendoerfer Prize, the Wisconsin MAA teaching award, and the MAA Haimo Award for Distinguished Mathematics Teaching, and was twice named Teacher of the Year at Beloit College. He is a co-author of three chapters in the NIST Handbook of Mathematical Functions, of Special Functions (with Andrews and Askey, Cambridge, 2010), and the author of Sources in the Development of Mathematics (Cambridge, 2011).

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.