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

9300389万本奖项支持万教授在数论方面的研究工作。数论中的一个基本问题是确定有限域上ζ函数的零点和极点的p进值。万教授建议对ζ函数族和l函数族进行系统的研究。一种方法是使用Dwork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。万教授希望解决关于指数和的L-函数的一般牛顿多边形的Adolphson-Sperber猜想，并证明关于超曲面的zeta函数的一般牛顿多边形的Dwork-Mazur猜想的强版本。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。＊＊＊

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. ***