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

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*Marvin Knopp; Mark Sheingorn*

# 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