Converse Theorems, Fune tor iality, and Applications to Number Theory
Converse Theorems, Fune tor iality, and Applications to Number Theory
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逆定理、函数性及其在数论中的应用
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
I. Piatetski
中科院分区：
文献类型：
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作者：
J. Cogdell;I. Piatetski
最近出现了GLn的匡威定理和控制自守L-函数的解析性质的Langlands-Shahidi方法，这使我们能够建立一些新的函性或自守形式的提升。在这篇文章中，我们将介绍匡威定理的现状，并概述使用匡威定理获得提升的方法。然后，我们将转向对新的提升及其应用的说明。
There has been a recent coming together of the Converse Theorem for GLn and the Langlands-Shahidi method of controlling the analytic properties of automorphic L-functions which has allowed us to establish a number of new cases of functoriality , or the lifting of automorphic forms. In this article we would like to present the current state of the Converse Theorem and outline the method one uses to apply the Converse Theorem to obtain liftings. We will then turn to an exposition of the new liftings and some of their applications.