Mathematical Sciences: Arithmetic Functions and their Applications

这项赠款支持教授埃利奥特在该地区的工作， 概率数论 具体而言，这一建议是 研究算术函数在指定序列上的值， 算术兴趣 除了其自身的优点，这些功能承担 在代数问题，并适用于算法的研究， 大整数的因式分解，以及密码学。 这是数论领域的研究。 数论 从整数和问题开始， 一个整数被另一个整数整除。 它是其中的 最古老的数学领域，它最初是追求 纯粹的美学原因。 然而，在过去的半个世纪里， 它已经成为开发新算法的重要工具， 计算机科学和新的电子纠错码。

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.