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Elliptic and Modular Functions from Gauss to Dedekind to Hecke

$64.00 ( ) USD

  • Date Published: March 2017
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9781108133784

$ 64.00 USD ( )
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  • 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
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    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

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    Product details

    • Date Published: March 2017
    • format: Adobe eBook Reader
    • isbn: 9781108133784
    • contains: 13 b/w illus.
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • 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).

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