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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.
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