Eisenstein Series, Operators and L-Functions

点击翻译按钮获取中文摘要

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.