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Number Theory and Modular Forms

Papers in Memory of Robert A. Rankin

  • Book
  • © 2003

Overview

Editors:
  1. Bruce Berndt

    1. Department of Mathematics, University of Illinois, Urbana, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Ken Ono

    1. Department of Mathematics, University of Wisconsin, Madison, USA

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Developments in Mathematics (DEVM, volume 10)

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Table of contents (27 chapters)

  1. Front Matter

    Pages i-8
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  2. The Life and Work of R.A. Rankin (1915–2001)

    • Bruce C. Berndt, Winfried Kohnen, Ken Ono
    Pages 9-38

  3. Memoir: My Cambridge Years

    • Robert A. Rankin
    Pages 39-42

  4. The De Morgan Medal

    • Bruce Berndt, Ken Ono
    Pages 43-44

  5. On the Petersson Norm of Certain Siegel Modular Forms

    • Youngju Choie, Winfried Kohnen
    Pages 45-48

  6. On Borcherds Products Associated with Lattices of Prime Discriminant

    • Jan Hendrik Bruinier, Michael Bundschuh
    Pages 49-61

  7. An L-Function of Degree 27 for Spin9

    • Daniel Bump, David Ginzburg
    Pages 63-78

  8. Representations of Integers as Sums of 32 Squares

    • Heng Huat Chan, Kok Seng Chua
    Pages 79-89

  9. Some Remarks on Signs in Functional Equations

    • Benedict H. Gross
    Pages 91-93

  10. On Dirichlet Series for Sums of Squares

    • Jonathan Michael Borwein, Kwok-Kwong Stephen Choi
    Pages 95-127

  11. Poincaré Series and Hilbert Modular Forms

    • Wenzhi Luo
    Pages 129-140

  12. On Non-Congruence Subgroups of the Analogue of the Modular Group in Characteristic p

    • A. W. Mason
    Pages 141-144

  13. On Modular Forms Arising from a Differential Equation of Hypergeometric Type

    • Masanobu Kaneko, Masao Koike
    Pages 145-164

  14. A Note on Base Change, Identities Involving Ï„(n), and a Congruence of Ramanujan

    • Solomon Friedberg
    Pages 165-168

  15. The Orders of Related Elements of a Finite Field

    • Stephen D. Cohen
    Pages 169-183

  16. On the Uniform Distribution of Certain Sequences

    • M. Ram Murty, Kotyada Srinivas
    Pages 185-192

  17. Modular Transformations of Ramanujan’s Fifth and Seventh Order Mock Theta Functions

    • Basil Gordon, Richard J. Mcintosh
    Pages 193-222

  18. Estimates for Sums of Coefficients of Dirichlet Series with Functional Equation

    • V. Kumar Murty
    Pages 223-233

  19. Rational Points on the Sphere

    • W. Duke
    Pages 235-239

  20. Estimating Additive Character Sums for Fuchsian Groups

    • Dorian Goldfeld, Cormac O’Sullivan
    Pages 241-267
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Keywords

About this book

Robert A. Rankin, one of the world's foremost authorities on modular forms and a founding editor of The Ramanujan Journal, died on January 27, 2001, at the age of 85. Rankin had broad interests and contributed fundamental papers in a wide variety of areas within number theory, geometry, analysis, and algebra. To commemorate Rankin's life and work, the editors have collected together 25 papers by several eminent mathematicians reflecting Rankin's extensive range of interests within number theory. Many of these papers reflect Rankin's primary focus in modular forms. It is the editors' fervent hope that mathematicians will be stimulated by these papers and gain a greater appreciation for Rankin's contributions to mathematics.
This volume would be an inspiration to students and researchers in the areas of number theory and modular forms.

Editors and Affiliations

  • Department of Mathematics, University of Illinois, Urbana, USA

    Bruce Berndt

  • Department of Mathematics, University of Wisconsin, Madison, USA

    Ken Ono

Bibliographic Information

  • Book Title: Number Theory and Modular Forms

  • Book Subtitle: Papers in Memory of Robert A. Rankin

  • Editors: Bruce Berndt, Ken Ono

  • Series Title: Developments in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-6044-6

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag US 2003

  • Hardcover ISBN: 978-1-4020-7615-2Published: 30 November 2003

  • Softcover ISBN: 978-1-4419-5395-7Published: 08 December 2010

  • eBook ISBN: 978-1-4757-6044-6Published: 11 November 2013

  • Series ISSN: 1389-2177

  • Series E-ISSN: 2197-795X

  • Edition Number: 1

  • Number of Pages: 400

  • Additional Information: Reprinted from THE RAMANUJAN JOURNAL, 7:1-3

  • Topics: Number Theory, Field Theory and Polynomials

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