**DIMACS - Series in Discrete Mathematics and Theoretical Computer Science**

Volume: 64;
2004;
264 pp;
Hardcover

MSC: Primary 11;

**Print ISBN: 978-0-8218-2703-1
Product Code: DIMACS/64**

List Price: $110.00

AMS Member Price: $88.00

MAA Member Price: $99.00

**Electronic ISBN: 978-1-4704-4022-0
Product Code: DIMACS/64.E**

List Price: $103.00

AMS Member Price: $82.40

MAA Member Price: $92.70

# Unusual Applications of Number Theory

Share this page *Edited by *
*Melvyn B. Nathanson*

A co-publication of the AMS and DIMACS

This volume contains the proceedings of the workshop held at
the DIMACS Center of Rutgers University (Piscataway, NJ) on Unusual
Applications of Number Theory. Standard applications of number theory
are to computer science and cryptology. In this volume, well-known
number theorist, Melvyn B. Nathanson, gathers articles from the
workshop on other, less standard applications in number theory, as
well as topics in number theory with potential applications in science
and engineering.

The material is suitable for graduate students and researchers interested in
number theory and its applications.

Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1–7 were co-published with the Association for Computer Machinery (ACM).

#### Readership

Graduate students and research mathematicians interested in number theory and applications.

# Table of Contents

## Unusual Applications of Number Theory

- Cover Cover11
- Title page i2
- Contents iii4
- Foreword v6
- Preface vii8
- A four parameter generalization of Göllnitz’s (big) partition theorem 110
- The Friedman-Joichi-Stanton monotonicity conjecture at primes 918
- A group theoretic approach to public-key cryptography 1726
- Dedekind sums: A combinatorial-geometric viewpoint 2534
- Noncommutative number theory 3746
- An application of structure theory of set addition to a question in ergodic theory 5362
- Linear algebra and additive theory 6170
- On the distribution of the power generator modulo a prime power 7180
- Number theoretical error estimates in a quantization scheme for bandlimited signals 8190
- Random walks with badly approximable numbers 95104
- Distribution of values of real quadratic zeta functions 103112
- Standardizing nonstandard methods for upper Banach density problems 109118
- On homogeneous linear recurrence relations and approximation of zeros of complex polynomials 125134
- Formal power series arising from multiplication of quantum integers 145154
- Formal languages and number theory 169178
- Lattices, cryptography, and the NTRU public key cryptosystem 183192
- Zeta functions of graph coverings 199208
- Comparison of Selberg’s trace formula with its discrete analogues 213222
- Unusual applications of quadratic Gaussian sums 227236
- Back Cover Back Cover1274