Langlands' Lifting from Orthogonal and Symplectic Groups to GL(n)

Piatetski-Shapiro 9704997这个奖项资助的研究的目的是研究正交群和辛群G的一般尖端自同构表示到GL(N)的自同构表示的提升。PI和他的合作者将使用的方法如下。首先，他们将构造G×GL(M)的L函数。之后，他们将应用GL(N)的逆定理。L函数应具有适当的函数方程和良好的解析性质。这一建议出现在被称为朗兰兹计划的数学部分。朗兰兹计划是数论的一部分。数论是研究整体数的性质的学科，是数学中最古老的分支。从一开始，数论中的问题就为在该学科的其他不同部分创造新的数学提供了动力。朗兰德的计划是一种将数论与微积分联系起来的一般哲学；它体现了研究整数的现代方法。现代数论是非常技术性和深刻性的，但它在理论计算机科学和编码理论等领域有着惊人的应用。

Piatetski-Shapiro 9704997 The objective of the research funded under this award is to investigate the lifting of generic cuspidal automorphic representations of orthogonal and symplectic groups G to automorphic representations of GL(n). The method that the PI and his collaborators will use is the following. First, they will construct L-functions for G x GL(m). After that, they will apply the converse theorem for GL(n). The L-functions should have the proper functional equation and good analytic properties. This proposal is in the part of mathematics known as the Langlands program. The Langlands program is part of Number Theory. Number Theory is the study of the properties of the whole numbers and is the oldest branch of mathematics. From the beginning problems in number theory have furnished a driving force in creating new mathematics in other diverse parts of the discipline. The Langland's program is a general philosophy that connects number theory with calculus; it embodies the modern approach to the study of whole numbers. Modern Number Theory is very technical and deep, but it has had astonishing applications in areas like theoretical computer science and coding theory.