Abstract
We consider a new construction of automorphic representations of GL2(A), using the general idea of automorphic descent methods. In particular, four families of examples are considered. The representations τ of GL2(A) are obtained from automorphic representations π on reductive groups H, which contain a reductive subgroup G of GSp2n. We give criteria for nonvanishing and for cuspidality of the constructed representations τ, in terms of periods or co-periods and by the holomorphy at s=1 of certain l-functions of π. We also calculate the relation of the unramified parameters in certain cases, which indicates that τ and π fit partially to the Langlands functorial principle. We prove some low-rank cases to support our conjectures.
Original language | English (US) |
---|---|
Pages (from-to) | 4779-4820 |
Number of pages | 42 |
Journal | International Mathematics Research Notices |
Volume | 2011 |
Issue number | 21 |
DOIs | |
State | Published - 2011 |
Bibliographical note
Funding Information:Foundation Founded by the Israel Academy of Sciences and Humanities Grant no. 210/10 (to D.S.).
Funding Information:
This work is supported in part by the NSF grant DMS-1001672 (to D.J.) and by the Israel Science