Analytic Number Theory on Groups

该奖项支持研究多里安戈德菲尔德在thestudy离散群体与应用到解析数论。所提出的研究涉及各种公开问题：Fuchsian群上的加性特征标的分布，ABC猜想，Ash-Borel模符号扭曲的高阶Eisensteineries，GL（2）的三次覆盖的Waldspurger对应，以及与L-级数导数相关的几何周期。数论有其历史根源于对整数的研究，是数学中最古老的分支之一。世纪的丢番图在他的算术中提出了许多问题，要求解是整数。方程整数解的研究现在被称为丢番图分析，并在计算复杂性、数据传输、信号处理、密码学、Goldfeld教授介绍并研究了新类型的几何L-级数（无穷和几何对象取决于一个复杂的参数），以开发一种新的一般方法来攻击迄今为止仍然未解决的丢番图问题的大类。

This award supports the research of Dorian Goldfeld in thestudy of discrete groups with applications to analytic numbertheory. The proposed research concerns various open problemsrelated to: the distribution of additive characters onFuchsian groups, the ABC-conjecture, higher rank Eisensteinseries twisted by Ash-Borel modular symbols, the Waldspurgercorrespondence for cubic covers of GL(2), and the geometricperiods associated to derivatives of L-series.Number theory has its historical roots in the study of wholenumbers, and is among the oldest branches of mathematics. Diophantus, of the third century, proposed many problems inhis arithmetic, requiring the solutions to be whole numbers.The study of integer solutions to equations is now referredto as Diophantine analysis, and has many applications tocomputational complexity, data transmission, signalprocessing, cryptography, etc. Professor Goldfeld introducesand studies new types of geometrical L-series (infinite sumsof geometric objects depending on a complex parameter) inorder to develop a novel general method to attack a largeclass of hitherto still unsolved Diophantine problems.