## Unusual Applications of Number Theory: DIMACS Workshop, Unusual Applications of Number Theory, January 10-14, 2000, DIMACS CenterThis 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. |

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### Contents

The FriedmanJoichiStanton monotonicity conjecture at primes | 11 |

a combinatorialgeometric viewpoint | 25 |

An application of structure theory of set addition to a question | 53 |

On the distribution of the power generator modulo a prime power | 71 |

Random walks with badly approximable numbers | 95 |

Standardi2ing nonstandard methods for upper Banach density problems | 109 |

On homogeneous linear recurrence relations and approximation of zeros | 125 |

Formal power series arising from multiplication of quantum integers | 145 |

Formal languages and number theory | 169 |

Lattices cryptography and the NTRU public key cryptosystem | 183 |

Zeta functions of graph coverings | 199 |

Comparison of Selbergs trace formula with its discrete analogues | 213 |

Unusual applications of quadratic Gaussian sums | 227 |

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