Mathematical Sciences: Zeta Functions and Automorphic Forms

这一建议的研究将是关于ζ函数和自同构形式的数论问题。自同构形式的傅里叶系数、爱森斯坦级数和某些ζ函数的特殊值是研究的主要对象。这是数论领域的研究。数论从整数和诸如整数能被整数整除之类的问题开始。它是数学中最古老的领域之一，最初纯粹出于审美原因而追求它。然而，在过去的半个世纪里，它已经成为开发计算机科学新算法和电子学新纠错码的重要工具。

The investigations of this proposal will be made on number- theoretical problems dealing with zeta functions and automorphic forms. The Fourier coefficients of automorphic forms, Eisenstein series, and the special values of certain zeta functions are the main objects of study. 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.