Mathematical Sciences: L-functions of Automorphic Forms and Applications

这项拨款支持Piatetski-Shapiro博士从事与Langland项目相关的项目。这些项目包括功能提升下的统一问题，并与广义拉马努金猜想的失效有关。第二个项目致力于从经典群到GL(n)的提升问题。第三个项目致力于在有限域上对Langland对应进行建模。这是数论领域的研究。数论从整数和诸如整数能被整数整除之类的问题开始。它是数学中最古老的领域之一，最初纯粹出于审美原因而追求它。然而，在过去的半个世纪里，它已经成为开发计算机科学新算法和电子学新纠错码的重要工具。

This grant supports the work of Dr. Piatetski-Shapiro to work on projects related to Langland's program. These projects include the problem of unitarity under functorial lifting and is related to the failure of the generalized Ramanujan conjecture. The second project is devoted to a problem of lifting from classical groups to GL(n). The third project is devoted to modelling Langland's correspondence over a finite field. This is research in the field of number theory. Number theory starts with the whole numbers and questions such as the divisibility of one whole number by another. It is among the oldest fields of mathematics and it was originally pursued for purely aesthetic reasons. However, within the last half century, it has become an essential tool in developing new algorithms for computer science and new error correcting codes for electronics.