eBook ISBN:  9780821877340 
Product Code:  CONM/143.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821877340 
Product Code:  CONM/143.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 143; 1993; 612 ppMSC: Primary 05; 11; 14; 33
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.
ReadershipGraduate students and specialists in number theory, modular functions, combinatorics and related analysis.

Table of Contents

Articles

David Bressoud, Marvin Knopp and Mark Sheingorn — In appreciation of Emil Grosswald [ MR 1210505 ]

Marvin Knopp and Mark Sheingorn — Ph.D. students of Emil Grosswald [ MR 1210506 ]

Marvin Knopp and Mark Sheingorn — Publications of Emil Grosswald [ MR 1210507 ]

Gert Almkvist — A rather exact formula for the number of plane partitions [ MR 1210508 ]

George E. Andrews — On Ramanujan’s empirical calculation for the RogersRamanujan identities [ MR 1210509 ]

Paul T. Bateman — Integers expressible in a given number of ways as a sum of two squares [ MR 1210510 ]

Bruce C. Berndt and James Lee Hafner — A theorem of Ramanujan on certain alternating series [ MR 1210511 ]

David M. Bressoud and ShiYuan Wei — Combinatorial equivalence of definitions of the Schur function [ MR 1210512 ]

Nancy Celniker, Steven Poulos, Audrey Terras, Cindy Trimble and Elinor Velasquez — Is there life on finite upper half planes? [ MR 1210513 ]

Yj. Choie and D. Zagier — Rational period functions for $\mathrm {PSL}(2, \mathbf {Z})$ [ MR 1210514 ]

L. Alayne Parson — Rational period functions and indefinite binary quadratic forms. III [ MR 1210515 ]

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 [ MR 1210516 ]

Harvey Cohn — Orbital modular equations [ MR 1210517 ]

Boris A. Datskovsky — A meanvalue theorem for class numbers of quadratic extensions [ MR 1210518 ]

Francine Delmer and JeanMarc Deshouillers — On a generalization of Farey sequences. I [ MR 1361694 ]

Harold G. Diamond, H. Halberstam and H.E. Richert — Sieve auxiliary functions. II [ MR 1210519 ]

W. Duke and H. Iwaniec — A relation between cubic exponential and Kloosterman sums [ MR 1210520 ]

Leon Ehrenpreis — Function theory for RogersRamanujanlike partition identities [ MR 1210521 ]

P. Erdős, D. J. Newman and J. Knappenberger — Forcing two sums simultaneously [ MR 1210522 ]

Ronald J. Evans, Kenneth B. Stolarsky and John J. Wavrik — Difference polynomials [ MR 1210523 ]

Jane E. Friedman — An application of Ehrenpreis’s basis method to the RogersRamanujan identities [ MR 1210524 ]

Janos Galambos — Extensions of some extremal properties of prime divisors to Poisson limit theorems [ MR 1210525 ]

Ellen Gethner — Rational period functions with irrational poles are not Hecke eigenfunctions [ MR 1210526 ]

Dorian Goldfeld and Jeffrey Hoffstein — On the number of Fourier coefficients that determine a modular form [ MR 1210527 ]

S. M. Gonek — An explicit formula of Landau and its applications to the theory of the zetafunction [ MR 1210528 ]

Basil Gordon and Kim Hughes — Multiplicative properties of $\eta $products. II [ MR 1210529 ]

Michael Grady and Morris Newman — Counting subgroups of given index in Hecke groups [ MR 1210530 ]

James Lee Hafner, Peter Sarnak and Kevin McCurley — Relatively prime values of polynomials [ MR 1210531 ]

Peter Hagis, Jr. — A new proof that every odd triperfect number has at least twelve prime factors [ MR 1210532 ]

John H. Hawkins and Marvin I. Knopp — A HeckeWeil correspondence theorem for automorphic integrals on $\Gamma _0(N)$, with arbitrary rational period functions [ MR 1210533 ]

J. Lehner — Lagrange’s theorem for Hecke triangle groups [ MR 1210534 ]

M. Ram Murty and V. Kumar Murty — Base change and the BirchSwinnertonDyer conjecture [ MR 1210535 ]

D. J. Newman — A “natural” proof of the nonvanishing of $L$series [ MR 1210536 ]

Andrew M. Odlyzko and Chris M. Skinner — Nonexistence of Siegel zeros in towers of radical extensions [ MR 1210537 ]

L. Alayne Parson — Modular integrals and indefinite binary quadratic forms [ MR 1210538 ]

Robert A. Rankin — Diagonalizing Eisenstein series. II [ MR 1210539 ]

David Rosen — Multiplier systems for the Hecke groups $G(\sqrt 2)$ and $G(\sqrt 3)$ [ MR 1210540 ]

Mark Sheingorn — Low height Hecke triangle group geodesics [ MR 1210541 ]

Thomas R. Shemanske and Lynne H. Walling — On the Shimura lift for Hilbert modular forms [ MR 1210542 ]

H. M. Stark — Dirichlet’s classnumber formula revisited [ MR 1210543 ]

Doron Zeilberger — Closed form (pun intended!) [ MR 1210544 ]

Doron Zeilberger — Gert Almkvist’s generalization of a mistake of Bourbaki [ MR 1210545 ]


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

Articles

David Bressoud, Marvin Knopp and Mark Sheingorn — In appreciation of Emil Grosswald [ MR 1210505 ]

Marvin Knopp and Mark Sheingorn — Ph.D. students of Emil Grosswald [ MR 1210506 ]

Marvin Knopp and Mark Sheingorn — Publications of Emil Grosswald [ MR 1210507 ]

Gert Almkvist — A rather exact formula for the number of plane partitions [ MR 1210508 ]

George E. Andrews — On Ramanujan’s empirical calculation for the RogersRamanujan identities [ MR 1210509 ]

Paul T. Bateman — Integers expressible in a given number of ways as a sum of two squares [ MR 1210510 ]

Bruce C. Berndt and James Lee Hafner — A theorem of Ramanujan on certain alternating series [ MR 1210511 ]

David M. Bressoud and ShiYuan Wei — Combinatorial equivalence of definitions of the Schur function [ MR 1210512 ]

Nancy Celniker, Steven Poulos, Audrey Terras, Cindy Trimble and Elinor Velasquez — Is there life on finite upper half planes? [ MR 1210513 ]

Yj. Choie and D. Zagier — Rational period functions for $\mathrm {PSL}(2, \mathbf {Z})$ [ MR 1210514 ]

L. Alayne Parson — Rational period functions and indefinite binary quadratic forms. III [ MR 1210515 ]

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 [ MR 1210516 ]

Harvey Cohn — Orbital modular equations [ MR 1210517 ]

Boris A. Datskovsky — A meanvalue theorem for class numbers of quadratic extensions [ MR 1210518 ]

Francine Delmer and JeanMarc Deshouillers — On a generalization of Farey sequences. I [ MR 1361694 ]

Harold G. Diamond, H. Halberstam and H.E. Richert — Sieve auxiliary functions. II [ MR 1210519 ]

W. Duke and H. Iwaniec — A relation between cubic exponential and Kloosterman sums [ MR 1210520 ]

Leon Ehrenpreis — Function theory for RogersRamanujanlike partition identities [ MR 1210521 ]

P. Erdős, D. J. Newman and J. Knappenberger — Forcing two sums simultaneously [ MR 1210522 ]

Ronald J. Evans, Kenneth B. Stolarsky and John J. Wavrik — Difference polynomials [ MR 1210523 ]

Jane E. Friedman — An application of Ehrenpreis’s basis method to the RogersRamanujan identities [ MR 1210524 ]

Janos Galambos — Extensions of some extremal properties of prime divisors to Poisson limit theorems [ MR 1210525 ]

Ellen Gethner — Rational period functions with irrational poles are not Hecke eigenfunctions [ MR 1210526 ]

Dorian Goldfeld and Jeffrey Hoffstein — On the number of Fourier coefficients that determine a modular form [ MR 1210527 ]

S. M. Gonek — An explicit formula of Landau and its applications to the theory of the zetafunction [ MR 1210528 ]

Basil Gordon and Kim Hughes — Multiplicative properties of $\eta $products. II [ MR 1210529 ]

Michael Grady and Morris Newman — Counting subgroups of given index in Hecke groups [ MR 1210530 ]

James Lee Hafner, Peter Sarnak and Kevin McCurley — Relatively prime values of polynomials [ MR 1210531 ]

Peter Hagis, Jr. — A new proof that every odd triperfect number has at least twelve prime factors [ MR 1210532 ]

John H. Hawkins and Marvin I. Knopp — A HeckeWeil correspondence theorem for automorphic integrals on $\Gamma _0(N)$, with arbitrary rational period functions [ MR 1210533 ]

J. Lehner — Lagrange’s theorem for Hecke triangle groups [ MR 1210534 ]

M. Ram Murty and V. Kumar Murty — Base change and the BirchSwinnertonDyer conjecture [ MR 1210535 ]

D. J. Newman — A “natural” proof of the nonvanishing of $L$series [ MR 1210536 ]

Andrew M. Odlyzko and Chris M. Skinner — Nonexistence of Siegel zeros in towers of radical extensions [ MR 1210537 ]

L. Alayne Parson — Modular integrals and indefinite binary quadratic forms [ MR 1210538 ]

Robert A. Rankin — Diagonalizing Eisenstein series. II [ MR 1210539 ]

David Rosen — Multiplier systems for the Hecke groups $G(\sqrt 2)$ and $G(\sqrt 3)$ [ MR 1210540 ]

Mark Sheingorn — Low height Hecke triangle group geodesics [ MR 1210541 ]

Thomas R. Shemanske and Lynne H. Walling — On the Shimura lift for Hilbert modular forms [ MR 1210542 ]

H. M. Stark — Dirichlet’s classnumber formula revisited [ MR 1210543 ]

Doron Zeilberger — Closed form (pun intended!) [ MR 1210544 ]

Doron Zeilberger — Gert Almkvist’s generalization of a mistake of Bourbaki [ MR 1210545 ]