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A Tribute to Emil Grosswald: Number Theory and Related Analysis
Edited by: Marvin Knopp and Mark Sheingorn
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Contemporary Mathematics
1993; 612 pp; softcover
Volume: 143
ISBN-10: 0-8218-5155-1
ISBN-13: 978-0-8218-5155-5
List Price: US$96
Member Price: US$76.80
Order Code: CONM/143
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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

  • In appreciation of Emil Grosswald; Ph.D. students of Emil Grosswald; Publications of Emil Grosswald
  • M. I. Knopp and M. Sheingorn -- Preface
  • G. Almkvist -- A rather exact formula for the number of plane partitions
  • G. E. Andrews -- On Ramanujan's empirical calculation for the Rogers-Ramanujan identities
  • P. T. Bateman -- Integers expressible in a given number of ways as a sum of two squares
  • B. C. Berndt and J. L. Hafner -- A theorem of Ramanujan on certain alternating series
  • D. M. Bressoud and S.-Y. Wei -- Combinatorial equivalence of definitions of the Schur function
  • N. Celnicker, S. Poulos, A. Terras, C. Trimble, and E. Velasquez -- Is there life on finite upper half planes?
  • Y. Choie and D. Zagier -- Rational period functions for \(PSL(2,{\mathbb Z})\)
  • L. A. Parson -- Rational period functions and indefinite binary quadratic forms, III
  • D. V. Chudnovsky and G. V. Chudnovsky -- Hypergeometric and modular function identities, and new rational approximations to and continued fraction expansions of classical constants and functions
  • H. Cohn -- Orbital modular equations
  • B. A. Datskovsky -- A mean-value theorem for class numbers of quadratic extensions
  • F. Delmer and J.-M. Deshouillers -- On a generalization of Farey sequences I
  • H. G. Diamond, H. Halberstam, and H.-E. Richert -- Sieve auxiliary functions II
  • W. D. Duke and H. Iwaniec -- A relation between cubic exponential and Kloosterman sums
  • L. Ehrenpreis -- Function theory for Rogers-Ramanujan-like partition identities
  • P. Erdös, D. J. Newman, and J. C. Knappenberger -- Forcing two sums simultaneously
  • R. J. Evans, K. B. Stolarsky, and J. J. Wavrik -- Difference polynomials
  • J. E. Friedman -- An application of Ehrenpreis's basis method to the Rogers-Ramanujan identities
  • J. Galambos -- Extensions of some extremal properties of prime divisors to Poisson limit theorems
  • E. Gethner -- Rational period functions with irrational poles are not Hecke eigenfunctions
  • D. Goldfeld and J. Hoffstein -- On the number of Fourier coefficients that determine a modular form
  • S. M. Gonek -- An explicit formula of Landau and its applications to the theory of the zeta-function
  • B. Gordon and K. Hughes -- Multiplicative properties of \(\eta\)-products II
  • M. Grady and M. Newman -- Counting subgroups of given index in Hecke groups
  • J. L. Hafner, P. Sernak, and K. McCurley -- Relatively prime values of polynomials
  • P. Hagis, Jr. -- A new proof that every odd triperfect number has at least twelve prime factors
  • J. H. Hawkins and M. I. Knopp -- A Hecke-Weil correspondence theorem for automorphic integrals on \(\Gamma _0(N)\), with arbitrary rational period functions
  • J. Lehner -- Lagrange's theorem for Hecke triangle groups
  • M. R. Murty and V. K. Murty -- Base change and the Birch-Swinnerton-Dyer conjecture
  • D. J. Newman -- A "natural" proof of the non-vanishing of L-series
  • A. M. Odlyzko and C. M. Skinner -- Nonexistence of Siegel zeros in towers of radical extensions
  • L. A. Parson -- Modular integrals and indefinite binary quadratic forms
  • R. A. Rankin -- Diagonalizing Eisenstein series, II
  • D. Rosen -- Multiplier systems for the Hecke groups \(G(\sqrt 2)\) and \(G(\sqrt 3)\)
  • M. Sheingorn -- Low height Hecke triangle group geodesics
  • T. R. Shemanske and L. H. Walling -- On the Shimura lift for Hilbert modular forms
  • H. M. Stark -- Dirichlet's class-number formula revisited
  • D. Zeilberger -- Closed form (pun intended!)
  • D. Zeilberger -- Gert Almkvist's generalization of a mistake of Bourbaki
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