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示理论方面的研究。这项工作涉及三个与数论的关系问题，这三个问题都有一个共同的主题-L的作用。主要集中在证明特殊线性群SL(2)上的尖点形式空间的重数为一的程序。第二个问题涉及一般线性群GL(N)的强多重数一定理的精细形式。最后，首席研究者试图完成对所有四元数下村曲面的泰特猜想的证明。从历史上看，自同构形起源于19世纪中叶的非欧几里德几何。因此，数学家和物理学家都早已认识到，许多具有根本重要性的物体本质上都是非欧几里得的。这个领域主要涉及关于整数的问题，但在使用几何和分析时，它保留了与其历史根源的联系，从而与理论物理中的规范理论和信息论中的编码理论等不同领域的问题有关。

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.