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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.
Foreword v
Preface vii
A four parameter generalization of Gollnitz's (big) partition theorem
K. ALLADI, G.E. ANDREWS, AND A. BERKOVICH
1(8)
The Friedman-Joichi-Stanton monotonicity conjecture at primes
GEORGE E. ANDREWS
9(8)
A group theoretic approach to public-key cryptography
IRIS ANSHEL, MICHAEL ANSHEL, BENJA FISHER, AND DORIAN GOLDFELD
17(8)
Dedekind sums: a combinatorial-geometric viewpoint
MATTHIAS BECK AND SINAI ROBINS
25(12)
Noncommutative number theory
PAULA B. COHEN
37(16)
An application of structure theory of set addition to a question in ergodic theory
JEAN-MARC DESHOUILLERS, GREGORY FREIMAN, AND ALEXANDER A. YUDIN
53(8)
Linear algebra and additive theory
J.A. DIAS DA SILVA
61(10)
On the distribution of the power generator modulo a prime power
JOHN B. FRIEDLANDER, JAN S. DT. HANSEN, AND IGOR E. SHPARLINSKI
71(10)
Number theoretical error estimates in a quantization scheme for bandlimited signals
C. SINAN GUNTURK
81(14)
Random walks with badly approximable numbers
DOUG HENSLEY AND FRANCIS EDWARD SU
95(8)
Distribution of values of real quadratic zeta functions
JOSHUA HOLDEN
103(6)
Standardizing nonstandard methods for upper Banach density problems
RENLING JIN
109(16)
On homogeneous linear recurrence relations and approximation of zeros of complex polynomials
BAHMAN KALANTARI
125(20)
Formal power series arising from multiplication of quantum integers
MELVYN B. NATHANSON
145(24)
Formal languages and number theory
JEFFREY SHALLIT
169(14)
Lattices, cryptography, and the NTRU public key cryptosystem
JOSEPH H. SILVERMAN
183(16)
Zeta functions of graph coverings
H.M. STARK AND A.A. TERRAS
199(14)
Comparison of Selberg's trace formula with its discrete analogues
AUDREY TERRAS
213(14)
Unusual applications of quadratic Gaussian sums
CARLOS JULIO MORENO AND AARON WAN
227