Eisenstein Series, Operators and L-Functions

Lagarias博士提出研究数论中与爱森斯坦级数和l函数相关的各种解析问题。有三个主题。第一个主题是关于lach ζ函数及其与爱森斯坦级数的关系。第二个主题是关于自同构l -函数上的某些de brange空间和相关算子的性质。第三个课题是研究各种非纯爱森斯坦级数的傅里叶系数。这个建议属于数论领域。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问题之间的相似之处，包括素数的分布，以及数学物理中的各种主题。本建议调查这类可能的联系。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。申请人正在培养相关领域的研究生。

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.