Mathematical Sciences: Multiplicity One Results for Automorphic Forms via L-functions

该奖项支持Dinakar Ramakrishnan教授在自同构形式和表征理论方面的研究。这项工作涉及到与数论有关的三个问题，它们以l函数为共同主题。重点研究了一类特殊线性群SL(2)上尖形空间的多重性证明程序。第二个问题涉及一般线性群GL(n)的强重性定理的精细版本。最后，主要研究者试图完成对所有四元数Shimura曲面的Tate猜想的证明。历史上，自同构形式起源于19世纪中期的非欧几里得几何。因此，数学家和物理学家很早就认识到，许多具有根本重要性的物体在其基本性质上是非欧几里得的。这个领域主要关注关于整数的问题，但在使用几何和分析时，它保留了与历史根源的联系，因此与理论物理中的规范理论和信息论中的编码理论等领域的问题联系在一起。

This award supports the research of Professor Dinakar Ramakrishnan in the theory of automorphic forms and representations. This work involves three problems with relations to number theory, which have L-functions as a common theme. The main focus is on a program to prove multiplicity one for the space of cusp forms on the special linear group SL(2). The second problem concerns fine versions of the strong multiplicity one theorem for the general linear group GL(n). Finally, the principal investigator seeks to complete a proof of the Tate conjecture for all quaternionic Shimura surfaces. Historically, automorphic forms arose out of non-Euclidean geometry in the middle of the nineteenth century. Both mathematicians and physicists have thus long realized that many objects of fundamental importance are non-Euclidean in their basic nature. This field is principally concerned with questions about the whole numbers, but in its use of geometry and analysis, it retains connection to its historical roots and thus to problems in areas as diverse as gauge theory in theoretical physics and coding theory in information theory.