Number Theory and Modular Forms

Papers in Memory of Robert A. Rankin

By: Bruce C. Berndt (Editor), Ken Ono (Editor)

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Hardcover | 30 November 2003

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412 Pages

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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.

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Preface	p. 5
The Life and Work of R. A. Rankin (1915-2001)	p. 9
Memoir: My Cambridge Years	p. 39
The De Morgan Medal	p. 43
On the Petersson Norm of Certain Siegel Modular Forms	p. 45
On Borcherds Products Associated with Lattices of Prime Discriminant	p. 49
An L-Function of Degree 27 for Spin[subscript 9]	p. 63
Representations of Integers as Sums of 32 Squares	p. 79
Some Remarks on Signs in Functional Equations	p. 91
On Dirichlet Series for Sums of Squares	p. 95
Poincare Series and Hilbert Modular Forms	p. 129
On Non-Congruence Subgroups of the Analogue of the Modular Group in Characteristic p	p. 141
On Modular Forms Arising from a Differential Equation of Hypergeometric Type	p. 145
A Note on Base Change, Identities Involving [tau](n), and a Congruence of Ramanujan	p. 165
The Orders of Related Elements of a Finite Field	p. 169
On the Uniform Distribution of Certain Sequences	p. 185
Modular Transformations of Ramanujan's Fifth and Seventh Order Mock Theta Functions	p. 193
Estimates for Sums of Coefficients of Dirichlet Series with Functional Equation	p. 223
Rational Points on the Sphere	p. 235
Estimating Additive Character Sums for Fuchsian Groups	p. 241
On the Signs of Fourier Coefficients of Cusp Forms	p. 269
On the Asymptotic Behaviour of General Partition Functions, II	p. 279
More Primes and Polynomials	p. 299
On the Generalized Rogers-Ramanujan Continued Fraction	p. 321
On the Parity of the Number of Partitions in Square Free Parts	p. 333
Relations Between the Ranks and Cranks of Partitions	p. 343
Perspectives de l'Approximation Diophantienne et de la Transcendance	p. 367
Partitions: At the Interface of q-Series and Modular Forms	p. 385
Table of Contents provided by Blackwell. All Rights Reserved.

Number Theory and Modular Forms

Papers in Memory of Robert A. Rankin

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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