Mathematical Sciences: Arithmetic Functions and their Applications

这笔赠款支持埃利奥特教授在概率数论领域的工作。具体地说，这个建议是研究指定的算术兴趣序列上的算术函数的值。除了它们本身的优点外，这些函数还涉及到代数中的问题，并适用于大整数因式分解算法的研究，因此也适用于密码学。这是数论领域的研究。数论始于整数和诸如一个整数被另一个整数整除的问题。它是最古老的数学领域之一，最初是出于纯粹的美学原因。然而，在过去的半个世纪里，它已经成为开发计算机科学的新算法和电子产品的新纠错码的必要工具。

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.