Collaborative Research: FRG: Applications of Multiple Dirichlet Series to Analytic Number Theory

合作研究：FRG：多重狄利克雷级数在解析数论中的应用

• 批准号: 0353964
• 负责人: Solomon Friedberg
• 金额: $ 12万
• 依托单位: Boston College
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-07-15 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0353964&HistoricalAwards=false
• 关键词: Collaborative; Research; FRG; Applications; Multiple

Abstract for Collaborative FRG proposals DMS- 0354534, DMS -0353964, DMS-0354662 and DMS-0354582 of Hoffstein, Bump Friedberg and GoldfeldThe object of this proposal is to continue todevelop the theory of multiple Dirichlet seriesalong a number of highly promising directions.These include the formulation of aclassification theory via Dynkin diagrams andmetaplectic forms, analysis of naturalconstructions as inner products of automorphic forms on GL(n),and investigating examples coming fromEisenstein series related to deformation theoryof universal elliptic curves. Manyapplications are expected to the analysis of various familiesof L-functions The theory of L-functions of one complex variable iscentral in modern number theory. Special values ofL-functions have provided links between such diverseareas of mathematics as algebraic geometry, topology,probability and statistics, the representation theory ofinfinite dimensional Lie groups, and mathematicalphysics. In contrast, the theory of L-functions ofseveral complex variables (multipleDirichlet series) is still in its infancy. A large part of thefoundational theory was developedby the PI's and Postdocs of this proposal, who havebeen collaborating in teams, over thelast twenty years. The accumulated scientific results,combined with a mass sustained joint effort of thePI's, now point to the possibility of major breakthroughs.There is also an additionaltraining component. Workshops will be held each yearas well as short courses aimed at attracting graduate students, postdocs, andmathematicians in related fields. The motivationwill be to categorize and advertisethe major accessible problems in the field, tomap out progress made, and to prepare theparticipants for research projects.

协作FRG提议DMS-0354534，DMS -0353964，DMS-0354662和DMS-0354582的摘要摘要hoffstein，bump Friedberg和Goldfeld的对象，该建议的对象将继续进行多个Diaicklet sepraction Diarogrumation the Diailderions torgrumation torgrumation torgrumation nirder diaremention。和metleplectic形式，将天然构造分析为GL（N）上的自动形式的内部产物，并研究了与通用椭圆曲线变形理论相关的Fromeisenstein系列的示例。人们期望对l功能的各个家族进行分析，其中一个复杂变量iScentral在现代数理论中的l功能理论。功能的特殊值提供了数学的多样性，例如代数几何，拓扑，概率和统计，源代表理论，维度尺寸谎言组和数学术语。相比之下，左旋复合变量（多重里称序列）的L功能理论仍处于起步阶段。该提案的PI和PostDocs开发了很大一部分的理论，他们在Thelast二十年内就在团队中合作。累积的科学结果，加上thepi的质量持续共同努力，现在指出了重大突破的可能性。还有一个额外的培训组成部分。 每年将举行讲习班，以及旨在吸引相关领域的研究生，博士后和女主教员的简短课程。动机将是在该领域中分类和宣传主要可访问的问题，取得进展，并为研究项目做准备。