Analytic aspects of L-functions and their applications

摘要本文主要从解析数论的角度，研究与GL(n)的Ramanujan-Selberg猜想有关的自同构形式和自同构l函数的解析方面以及算术群上的量子唯一遍历性。本提案所讨论的问题是重要的未决问题，解决这些问题将对我们对基本理论的全貌的理解产生深远的影响。在最新进展的推动下，本项目的目标是通过改进现有技术和探索新方法来对这些基本问题做出贡献。

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.