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Unusual Applications of Number Theory
Edited by: Melvyn B. Nathanson, Herbert H. Lehman College, CUNY, New York, NY
A co-publication of the AMS and DIMACS.
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DIMACS: Series in Discrete Mathematics and Theoretical Computer Science
2004; 264 pp; hardcover
Volume: 64
ISBN-10: 0-8218-2703-0
ISBN-13: 978-0-8218-2703-1
List Price: US$98
Member Price: US$78.40
Order Code: DIMACS/64
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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

  • K. Alladi, G. E. Andrews, and A. Berkovich -- A four parameter generalization of Göllnitz's (big) partition theorem
  • G. E. Andrews -- The Friedman-Joichi-Stanton monotonicity conjecture at primes
  • I. Anshel, M. Anshel, B. Fisher, and D. Goldfeld -- A group theoretic approach to public-key cryptography
  • M. Beck and S. Robins -- Dedekind sums: A combinatorial-geometric viewpoint
  • P. B. Cohen -- Noncommutative number theory
  • J.-M. Deshouillers, G. A. Freiman, and A. A. Yudin -- An application of structure theory of set addition to a question in ergodic theory
  • J. A. Dias da Silva -- Linear algebra and additive theory
  • J. B. Friedlander, J. S. d. Hansen, and I. E. Shparlinski -- On the distribution of the power generator modulo a prime power
  • C. S. Güntürk -- Number theoretical error estimates in a quantization scheme for bandlimited signals
  • D. Hensley and F. E. Su -- Random walks with badly approximable numbers
  • J. Holden -- Distribution of values of real quadratic zeta functions
  • R. Jin -- Standardizing nonstandard methods for upper Banach density problems
  • B. Kalantari -- On homogeneous linear recurrence relations and approximation of zeros of complex polynomials
  • M. B. Nathanson -- Formal power series arising from multiplication of quantum integers
  • J. Shallit -- Formal languages and number theory
  • J. H. Silverman -- Lattices, cryptography, and the NTRU public key cryptosystem
  • H. M. Stark and A. A. Terras -- Zeta functions of graph coverings
  • A. Terras -- Comparison of Selberg's trace formula with its discrete analogues
  • C. J. Moreno and A. Wan -- Unusual applications of quadratic Gaussian sums
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