Mathematical Sciences: Topics in Analytic and Algorithmic Number Theory

该基金支持C. Pomerance、Helmut Maier和Andrew Granville教授在分析、计算和加性数论方面的研究。Pomerance教授将继续研究整数分解算法，特别是数字字段筛。Maier教授将研究周期多项式系数的大小和素数分布的不规则性。格兰维尔教授还将研究质数的分布以及筛理论。这是数论领域的研究。数论从整数和诸如整数能被整数整除之类的问题开始。它是数学中最古老的领域之一，最初纯粹出于审美原因而追求它。然而，在过去的半个世纪里，它已经成为开发计算机科学新算法和电子学新纠错码的重要工具。

This grant supports the research of Professors C. Pomerance, Helmut Maier and Andrew Granville to work on problems in analytic, computational, and additive number theory. Professor Pomerance will continue to work on integer factoring algorithms, in particular the number field sieve. Professor Maier will work on the size of the coefficients of cyclotomic polynomials and irregularities in the distribution of primes. Professor Granville will also work on the distributions of the primes as well as sieve theory. This is research in the field of number theory. Number theory starts with the whole numbers and questions such as the divisibility of one whole number by another. It is among the oldest fields of mathematics and it was originally pursued for purely aesthetic reasons. However, within the last half century, it has become an essential tool in developing new algorithms for computer science and new error correcting codes for electronics.