Mathematical Sciences: Probabilistic Diophantine Approximation

PI将研究数论中几个不同但相互关联的问题。第一部分将集中讨论非齐次Pell不等式积分解的渐近行为。该方案的另一部分涉及对上述部分的全局版本的研究，即计算倾斜矩形中的晶格点的数目。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。

The PI will investigate several different, yet mutually connected problems in number theory. One part will focus on the asymptotic behavior of integral solutions to inhomogeneous Pell inequalities. Another part of this proposal deals with the study of the global version to the part just described, namely, counting the number of lattice points in tilted rectangles. 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.