L-functions and Operators

Lagarias博士建议研究数论中与zeta和l函数相关的各种分析问题。有三个主题。第一个课题是研究Li系数族及其与自同构表示的相容性。第二个主题是在整个函数的Hilbert空间框架下解释自同构l函数的零，以及相关算子的研究。第三个课题是研究van der Geer和Schoof涉及自同构形式的两变量zeta函数的推广。这个建议属于数学的一般领域，叫做数论。这项工作研究了与素数分布有关的各种问题。这些包括可能用数学物理方程来描述它的一些特性。数论是一个古老的领域，近年来在通信、编码理论和密码学中提供了许多有用的应用。某些加密程序的性能——确保互联网通信安全所必需的——与质数分布上的微妙问题有关。这里处理的问题重叠了不同的数学领域，这项研究可能会刺激这些领域的研究人员之间的互动。

Dr. Lagarias proposes to study various analytic problems related to zeta and L-functions in number theory. There are three topics. The first topic is the study of Li coefficients as a family and their compatiblity with automorphic representations. The second topic concerns interpreting zeros of automorphic L-functions in the framework of Hilbert spaces of entire functions, and study of associated operators. The third topic is the study of generalizations of a two-variable zeta function of van der Geer and Schoof involving automorphic forms. This proposal is in the general area of mathematics called number theory. This work studies various problems associated to the distribution of prime numbers. These include possible description of some of its properties in terms of equations in mathematical physics. Number theory is an old field which in recent years has provided many useful applications in communications, coding theory and cryptography. The performance of some cryptographic procedures-necessary to secure internet communications - are related to subtle problems on the distribution of prime numbers. The questions treated here overlap different fields of mathematics and this research may stimulate interactions between researchers in these fields.