**Contemporary Mathematics**

Volume: 143;
1993;
612 pp;
Softcover

MSC: Primary 05; 11; 14; 33;

Print ISBN: 978-0-8218-5155-5

Product Code: CONM/143

List Price: $101.00

AMS Member Price: $80.80

MAA Member Price: $90.90

**Electronic ISBN: 978-0-8218-7734-0
Product Code: CONM/143.E**

List Price: $101.00

AMS Member Price: $80.80

MAA Member Price: $90.90

# A Tribute to Emil Grosswald: Number Theory and Related Analysis

Share this page *Edited by *
*Marvin Knopp; Mark Sheingorn*

Emil Grosswald was a mathematician of great accomplishment and remarkable breadth of vision. This volume pays tribute to the span of his mathematical interests, which is reflected in the wide range of papers collected here. With contributions by leading contemporary researchers in number theory, modular functions, combinatorics, and related analysis, this book will interest graduate students and specialists in these fields. The high quality of the articles and their close connection to current research trends make this volume a must for any mathematics library.

#### Readership

Graduate students and specialists in number theory, modular functions, combinatorics and related analysis.

# Table of Contents

## A Tribute to Emil Grosswald: Number Theory and Related Analysis

- Contents v6 free
- Preface viii9 free
- In appreciation of Emil Grosswald 110 free
- Ph.D. students of Emil Grosswald 918
- Publications of Emil Grosswald 1120
- A rather exact formula for the number of plane partitions 2130
- On Ramanujan's empirical calculation for the Rogers-Ramanujan identities 2736
- Integers expressible in a given number of ways as a sum of two squares 3746
- A theorem of Ramanujan on certain alternating series 4756
- Combinatorial equivalence of definitions of the Schur function 5968
- Is there life on finite upper half planes? 6574
- Rational period functions for PSL(2, z) 8998
- Rational period functions and indefinite binary quadratic forms , III 109118
- Hypergeometric and modular function identities, and new rational approximationsto and continued fraction expansions of classical constants and functions 117126
- Orbital modular equations 163172
- A mean-value theorem for class numbers of quadratic extensions 179188
- On a generalization of Farey sequences, I 243252
- Sieve auxiliary functions II 247256
- A relation between cubic exponential and Kloosterman sums 255264
- Function theory for Rogers-Ramanujan-like partition identities 259268
- Forcing two sums simultaneously 321330
- Difference polynomials 329338
- An application of Ehrenpreis's basis method to the Rogers-Ramanujan identities 347356
- Extensions of some extremal properties of prime divisors to Poisson limit theorems 363372
- Rational period functions with irrational poles are not Heeke eigenfunctions 371380
- On the number of Fourier coefficients that determine a modular form 385394
- An explicit formula of Landau and its applications to the theory of the zeta-function 395404
- Multiplicative properties of η-products II 415424
- Counting subgroups of given index in Heeke groups 431440
- Relatively prime values of polynomials 437446
- A new proof that every odd triperfect number has at least twelve prime factors 445454
- A Hecke-Weil correspondence theorem for automorphic integrals on Γ0(N), with arbitrary rational period functions 451460
- Lagrange's theorem for Heeke triangle groups 477486
- Base change and the Birch-Swinnerton-Dyer conjecture 481490
- A "natural" proof of the non-vanishing of L-series 495504
- Nonexistence of Siegel zeros in towers of radical extensions 499508
- Modular integrals and indefinite binary quadratic forms 513522
- Diagonalizing Eisenstein series, II 525534
- Multiplier systems for the Heeke groups G(√2) and G( √3) 539548
- Low height Heeke triangle group geodesics 545554
- On the Shimura lift for Hilbert modular forms 561570
- Dirichlet's class-number formula revisited 571580
- Closed form (pun intended!) 579588
- Gert Almkvist's generalization of a mistake of Bourbaki 609618