Mathematical Sciences: Analysis on Groups and Number Theory

这笔赠款支持P. Sarnak教授的研究， 首席研究员和博士Zeev Rudnick作为博士后 合伙人 Sarnak教授将研究 自守形式及其在数论中的应用 组合学 他希望能向将军取得进展 Ramanujan猜想 鲁德尼克博士正在自守 forms. 他打算应用从研究中获得的技术， 自守形式来计数仿射簇上的整数点。 他还研究欧拉产品的行为。 这是广义数论领域的研究 怀孕了 数论从整数开始， 例如一个整数被 另 它是最古老的数学领域之一， 最初是出于纯粹的美学原因。 然而没过 在过去的半个世纪，它已成为一个重要的工具， 为计算机科学和新的错误开发新的算法 纠正电子产品的代码。

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.