Eisenstein Series, Operators and L-Functions

0801029艾森斯坦级数、算子和L函数拉加里亚斯博士建议研究数论中与艾森斯坦级数和L函数有关的各种分析问题。全文共分三个主题。第一个主题涉及Lerch Zeta函数及其与Eisenstein级数的关系。第二个主题是关于某些De Brange空间和伴随于自同构L-函数的相关算子的性质。第三个主题是研究各种非全纯Eisenstein级数的傅里叶系数。这一建议属于数论领域。近年来，数论在通信、编码理论和密码学中提供了许多有用的应用。最近的发展已经观察到数论中的问题，包括素数的分布，与数学物理中的各种主题之间的相似之处。这项提案调查了这类可能的联系。所考虑的问题可能会刺激这些领域的研究人员之间的互动。提名者正在培训相关领域的研究生。

DMS-0801029 Eisenstein Series, Operators and L-Functions Dr. Lagarias proposes to investigate various analytic problems related to Eisenstein series and L-functions in number theory. There are three topics. The first topic concerns the Lerch zeta function and its relation to Eisenstein series. The second topic concerns properties of certain de Branges spaces and associated operators attached to automorphic L-functions. A third topic is to investigate Fourier coefficients of various nonholomorphic Eisenstein series.This proposal is in the area of number theory. Number theory has in recent years has provided many useful applications in communications, coding theory and cryptography. Recent developments have observed parallels between problems in number theory, including the distribution of prime numbers, and various topics in mathematical physics. This proposal investigates possible connections of this kind. The problems considered may stimulate interactions between researchers in these fields. The proposer is training graduate students in related areas.