DIMACS Series in
Discrete Mathematics and Theoretical Computer Science

VOLUME Sixty Four
TITLE: "Unusual Applications of Number Theory"
EDITORS: Melvyn B. Nathanson

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PREFACE

These are the proceedings of the DIMACS Workshop on Unusual Applications of Number Theory, which was held at the DIMACS Center of Rutgers University in Piscataway, New Jersey, on January 10-14, 2000. The usual applications of number theory are to computer science and crytology. In this workshop, the organizers looked for other applications of number theory, as well as topics in number theory with potential applications in science and engineering.

The organizing committee of this workshop was Mel Nathanson(Chair), George Andrews, David Chudnovsky, Ron Graham, Jeff Lagarias, Victor Miller, Andrew Odlyzko, and Carl Pomerance. I thank the members of this committee for their help in suggesting and inviting speakers to this meeting.

Partial support for this conference was provided by the National Science Foundation and the New Jersey Commission on Scienc and Technology.

TABLE OF CONTENTS


Forward                                                                        v
Preface                                                                      vii

A four parameter generalization of Gollnitz's (big) partition theorem
	K. Alladi, G. E. Andrews, and A. Berkovich            		       1

The Friedman-Joichi-Stanton monotonicity conjecture at primes
	George E. Andrews						       9

A group theoretic approach to public-key cryptography
	Iris Anshel, Michael Anshel, Benji Fisher, and Dorian Goldfeld	      17

Dedekind sums: a combinatorial-geometric viewpoint
	Matthias Beck and Sinai Robins					      25

Noncommutative number theory
	Paula B. Cohen							      37

An application of structure of set addition to a question in ergodic theory
	Jean-Marc Deshouillers, Gregory Freiman, and Alexander A. Yudin	      53

Linear algebra and addictive theory
	J. A. Dias Da Silva						      61

On the distribution of the power generator modulo a prime power
	John B. Freidlander, Jan S. T. Hansen, and Igor E. Shparlinski	      71

Number theoretical error estimates in a quantization scheme
	for bandlimited signals
	C. Sinan Gunturk						      81

Random walks with badly approximable numbers
	Doug Hensley and Francis Edward Su				      95

Distribution of values of real quadratic zeta functions			            
	Joshua Holden						             103

Standardizing nonstandard methods for upper Banach density problems
	Renling Jin							     109

On homogeneous linear recurrence relations and approximation of zeros
 	of complex polynomials
	Bahman Kalantari						     125

Formal power series arising from multiplication of quantum integers
	Melvin B. Nathanson 						     145

Formal languages and number theory
	Jeffrey Shallit							     169

Lattices, cryptography, and the NTRU public key cryptosystem
	Joseph H. Silverman						     183

Zeta functions of graph coverings
	H. M. Stark and A. A. Terras					     199

Comparison of Selberg's trace formula with its discrete analogues
	Audrey Terras							     213

Unusual applications of quadratic Gaussian sums
	Carlos Julio Moreno and Aaron Wan				     227
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Document last modified on April 14, 2004.