L-Functions and Automorphic Forms Conference, May 16 - 19, 2002, The Johns Hopkins University

ζ函数和l函数为研究数论中的困难和基本问题提供了一种极其强大的方法。此外，类似的函数在数学和物理的其他部分也得到了支持，例如，为看似不同的数据提供正则化。自同构形式的动态场是重要zeta函数的极好来源，事实上，Langlands的一个深远的猜想说，所有承认欧拉积的zeta函数都是模的，即与GL(n)上的自同构形式相关联。本次会议将回顾和研究过去几年来取得的积极成果和技术，特别关注导致自同构形式从一个群转移到另一个群的各种实例的l -函数方法。这个奖部分地支持了一个数论会议。数论是研究数字性质的数学分支，如质数的分布。这次特别的会议关注于某些类型的连续函数，称为自同态函数，它编码自然界中发生的深层对称性，类似于小池塘上的波形。出现的离散音调具有有趣的数论意义。数学家和物理学家可以从离散的数字集合开始，并从中构建连续函数，而不是从函数开始寻找它们的离散音调。然后，中心问题是知道这些函数是否承认隐藏的对称性。当它们这样做时，还必须存在更多的特殊属性。开发这类信息是一项紧迫的工作，还有许多金矿尚未被发现。

Zeta and L-functions provide an extremely powerful method for studying difficult and fundamental problems in Number theory. Moreover, analogous functions are propping up in other parts of Mathematics as well as inPhysics, for example to provide regularizations of seemingly divergent data.The dynamic field of Automorphic Forms is an excellent source of important zeta functions, and in fact a far-reaching conjecture of Langlands says that all zeta functions admitting an Euler product are modular, i.e., associated to automorphic forms on GL(n). This conference will review and examine the positive results and techniques which have come about in the past few years, with a special eye towards the L-function methods leading to various instances of transfer of automorphic forms from one group to another.This award partially supports a conference in number theory. Number theory is that branch of mathematics that studies properties of numbers, such as the distribution of prime numbers. This particular conference focuses on certain types of continuous functions, called automorphic functions, that encode deep symmetries which occur in nature, analogous to waveforms on a small pond. The discrete tones which occur have interesting number theoretic meanings. Instead of starting with the functions and looking for their discrete tones, mathematicians and physicists can start with discrete collections of numbers and from which they construct continuous functions. Then the central problem is to know if these functions admit hidden symmetries. When they do, then still more special properties must be present as well. Exploiting this kind of information is a pressing endeavor and there are many gold mines yet to be discovered.