Number Theory and Modular Forms

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 τ(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

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.

• Lattice
• Prime
• continued fraction
• finite field
• number theory

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

  Bruce Berndt

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

  Ken Ono

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