On linear periods
By Chong-Quan Zhang. 2013
76 citations recorded by the source corpus.
Let $$\pi '$$π′ be a cuspidal automorphic representation of $${\mathrm{GL}}_{2n}({\mathbb {A}})$$GL2n(A), which is assumed to be the Jacquet–Langlands transfer from a cuspidal automorphic representation $$\pi $$π of $${\mathrm{GL}}_{2m}(D)({\mathbb {A}})$$GL2m(D)(A), where $$D$$D is a division algebra so that $${\mathrm{GL}}_{2m}(D)$$GL2m(D) is an inner form of $${\mathrm{GL}}_{2n}$$GL2n. In this paper, we consider the relation between linear periods on $$\pi $$π and $$\pi '$$π′. We conjecture that the non-vanishing of the linear period on $$\pi $$π would imply the non-vanishing of that on $$\pi '$$π′. We illustrate an approach using a relative trace formula towards this conjecture, and prove the existence of smooth transfer over non-archimedean local fields.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2ad85d9e1fe8e9a619f8c90e50934a17d9f56cc8
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- On the arithmetic of Shalika models and the critical values of L-functions for GL2n (2011, methodology): “It relates the period-integral over H of a cusp form ϕ of G to a certain zeta-integral of the function Sηψ(ϕ) in the Shalika model corresponding to ϕ over one copy of GLn. Proposition 3.1.5 (Friedberg–Jacquet, [13] Prop.”
- On the local Bump-Friedberg L-function (2013, background): “of [11], which applies to any irreducible π such that HomSn(π, θ) 6= 0 thanks to Lemma 6.”