Mathematical Sciences: Analytic Methods for Automorphic Forms

Iwaniec教授和他的博士后助理杜克博士将使用解析数论的方法来研究模形式和自同构形；特别是，Iwaniec博士将继续他的长期项目，通过指数和来完善模形式理论。解析数论的领域适用于整数的离散领域。依赖于连续性和极限概念的分析技术起源于微积分。使用连续方法研究离散数的想法已经有两百年的历史了，但随着伊万尼奇教授等现代分析数论家的工作，该领域获得了新的新生。

Professor Iwaniec and his postdoctoral associate Dr. Duke will use the methods of Analytic Number Theory to investigate modular and automorphic forms; in particular, Dr. Iwaniec will continue his longterm project of refining the theory of modular forms by means of exponential and character sums. The field of Analytic Number Theory applies to the discrete realm of the whole numbers the techniques of Analysis, dependent on the notions of Continuity and Limit, originating in Calculus. The idea of using continuous methods to investigate the Discrete is two centuries old, but with the work of the modern analytic number theorists such as Professor Iwaniec, the field has had a new rebirth.