Analytic aspects of L-functions and their applications

L-函数的解析方面及其应用

• 批准号: 0245258
• 负责人: Wenzhi Luo
• 金额: $ 14.46万
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-01 至 2006-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0245258&HistoricalAwards=false
• 关键词: Analytic; aspects; functions; their; applications

DMS-0245258Luo, WenzhiAbstractTitle: Analytic aspects of L-functions and their applications This proposal is primarily concerned with the analytic aspects of automorphic forms and automorphic L-functions related to the Ramanujan-Selberg conjecture for GL(n) and the quantum unique ergodicity onarithmetic groups, from the perspectives of analytic number theory. The questions addressed to in this proposal are important open questions,the resolution of which would have profound impact on our understanding of the complete picture of the underlying theories. Motivated by recent advance, the goal of the present projects is to make contributions to these fundamental problems by refining current techniques and by exploring new approaches.

L-函数的解析性质及其应用 本文主要从解析数论的角度研究了与GL（n）的Ramanujan-Selberg猜想有关的自守形式和自守L-函数的解析性质以及算术群的量子唯一遍历性。 这个建议所涉及的问题是重要的未决问题，这些问题的解决将对我们理解基本理论的全貌产生深远的影响。受最新进展的推动，本项目的目标是通过改进现有技术和探索新方法来为这些基本问题做出贡献。