Automorphic Plancherel density theorem

作者：Shin Sug Woo^*

来源：Israel Journal of Mathematics, 2012, 192(1): 83-120.

DOI：10.1007/s11856-012-0018-z

Let F be a totally real field, G a connected reductive group over F, and S a finite set of finite places of F. Assume that G(F aSu(a"e) a"e) has a discrete series representation. Building upon work of Sauvageot, Serre, Conrey-Duke-Farmer and others, we prove that the S-components of cuspidal automorphic representations of are equidistributed with respect to the Plancherel measure on the unitary dual of G(F (S) ) in an appropriate sense. A few applications are given, such as the limit multiplicity formula for local representations in the global cuspidal spectrum and a quite flexible existence theorem for cuspidal automorphic representations with prescribed local properties. When F is not a totally real field or G(F aSu(a"e) a"e) has no discrete series, we present a weaker version of the above results.

• 出版日期2012-11