**Contemporary Mathematics**

Volume: 166;
1994;
369 pp;
Softcover

MSC: Primary 11;

Print ISBN: 978-0-8218-5173-9

Product Code: CONM/166

List Price: $76.00

AMS Member Price: $60.80

MAA Member Price: $68.40

**Electronic ISBN: 978-0-8218-7757-9
Product Code: CONM/166.E**

List Price: $76.00

AMS Member Price: $60.80

MAA Member Price: $68.40

# The Rademacher Legacy to Mathematics

Share this page *Edited by *
*George E. Andrews; David M. Bressoud; L. Alayne Parson*

This book contains papers presented at the Hans Rademacher Centenary Conference, held at Pennsylvania State University in July 1992. The astonishing breadth of Rademacher's mathematical interests is well represented in this volume. The papers collected here range over such topics as modular forms, partitions and \(q\)-series, Dedekind sums, and Ramanujan type identities. Rounding out the volume is the opening paper, which presents a biography of Rademacher. This volume is a fitting tribute to a remarkable mathematician whose work continues to influence mathematics today.

#### Readership

Research mathematicians.

# Table of Contents

## The Rademacher Legacy to Mathematics

- Contents vii8 free
- Preface xi12 free
- Hans Rademacher 1892–1969 xiii14 free
- On Rademacher's multiplier system for the classical theta-function 138 free
- Application of Dedekind eta-multipliers to modular equations 946
- Singularities, functional equations, and the circle method 3572
- On Weyl's inequality for eigenvalues 81118
- The GL(2) Rankin-Selberg convolution for higher level non-cuspidal forms 83120
- Congruences on the Fourier coefficients of modular forms on Γ0(N) 93130
- Diagonalizing Eisenstein series IV 107144
- Generalized Dedekind η-products 119156
- Vanishing coefficients in the expansion of products of Rogers-Ramanujan type 129166
- Schur's theorem, Capparelli's conjecture and q-trinomial coefficients 141178
- Modified convergence for q-continued fractions defined by functional relations 155192
- A simple proof of an Aomoto type extension of the q-Morris theorem 167204
- Congruences for certain generalized Frobenius partitions modulo p3 183220
- Some asymptotic formulae for Ramanujan's mock theta functions 189226
- On the distribution of Dedekind sums 197234
- Wilf's conjecture and a generalization 211248
- An elementary proof of Wilf's conjecture 235272
- Cubic modular identities of Ramanujan, hypergeometric functions and analogues of the arithmetic-geometric mean iteration 245282
- Residue periodicity in subgroup counting functions 265302
- Addition theorems for σ-finite groups 275312
- On sums of three integral cubes 285322
- A note on character sums 295332
- Large factors of small polynomials 301338
- Factors of period polynomials for finite fields, I 309346
- The Phragmén-Lindelöf theorem and modular elliptic curves 335372
- Multidimensional beta and gamma integrals 341378
- Rademacher, calculus of variations, inequalities, and relative error 359396