Mathematical Sciences: Zeta Functions and L-Functions over Finite Fields

9300389该奖项支持万教授从事数论研究。数论中的一个基本问题是确定有限域上Zeta函数的零点和极点的p-ady值。万教授建议对Zeta函数族和L函数族进行系统的研究。一种方法是使用德沃克的p-进理论。一个新的关键因素是从线性规划中引入了一些最大化函数。万教授期望解决关于指数和的L函数的广义牛顿多边形的Adolphson-Sperber猜想，并证明关于超曲面的zeta函数的广义牛顿多边形的Dwork-Mazur猜想的一个强版本。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。***

9300389 Wan This award supports the research of Professor Wan to work in number theory. A basic question in number theory is to determine the p-adic values of the zeros and poles of zeta functions over finite fields. Professor Wan proposes to give a systematic investigation of this question for families of zeta functions and L-functions. One method is to use Dwork's p-adic theory. A new key ingredient is the introduction of some maximizing functions from linear programming. Professor Wan expects to resolve the Adolphson-Sperber conjecture about the generic Newton polygon of L- functions of exponential sums and prove a strong version of the Dwork-Mazur conjecture about the generic Newton polygon of zeta functions of hypersurfaces. 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. ***