Mathematical Sciences: Analysis on Groups and Number Theory

这笔赠款支持P.Sarnak教授作为首席研究员和Zeev Rudnick博士作为博士后助理进行的研究。萨纳克教授将致力于自同构型的谱理论及其在数论和组合学中的应用。他希望在拉马努扬猜想方面取得进展。鲁德尼克博士正在研究自我同构的形式。他打算将研究自同构形的技术应用于仿射簇上的整点计数。他还在调查欧拉产品的行为。这是数论领域的广泛研究。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 the research of Professor P. Sarnak as principal investigator and Dr. Zeev Rudnick as a post-doctoral associate. Professor Sarnak will work on the spectral theory of automorphic forms and its applications to number theory and combinatorics. He hopes to make progress towards the general Ramanujan conjecture. Dr. Rudnick is working in automorphic forms. He intends to apply techniques derived from the study of automorphic forms to counting integer points on affine varieties. He is also investigating the behavior of Euler products. This is research in the field of number theory broadly conceived. 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.