Mathematical Sciences: Arithmetic Functions and their Applications

这笔经费支持艾略特教授在概率数论领域开展工作。具体地说，这个提议是研究等差兴趣的规定序列上的等差函数的值。除了它们自身的优点外，这些函数还涉及代数问题，并适用于大整数分解算法的研究，因此也适用于密码学。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 Professor Elliott to work in the area of probabilistic number theory. Specifically, this proposal is to study the values of arithmetic functions on prescribed sequences of arithmetic interest. Besides their own merit, such functions bear upon problems in algebra, and apply to the study of algorithms for the factorization of large integers, and so to cryptography. 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.