On linear periods

2013/07/29 by Chong Zhang, Zhang, Chong · 3 citations
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1307.7570

to appear in Mathematische Zeitschrift

arxiv created 2014/11/24 · arxiv updated 2014/11/25

Abstract

Let π' be a cuspidal automorphic representation of GL_2n, which is assumed to be the Jacquet-Langlands transfer from a cuspidal automorphic representation π of GL_2m(D), where D is a division algebra so that GL_2m(D) is an inner form of GL_2n. In this paper, we consider the relation between linear periods on π and π'. We conjecture that the non-vanishing of the linear period on π would imply the non-vanishing of that on 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.

Cited by

• Un caractère relatif pondéré
• Parahoric level p-adic L-functions for automorphic representations of GL_2n with Shalika models
• On the relative Langlands duality for Sp_2n \backslash GL_2n+1 (with an appendix by Zeyu Wang)

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• Cuspidal representations of quaternionic GL_n(D) with symplectic periods
• Intertwining periods, L-functions and local-global principles for distinction of automorphic representations
• On Shalika Periods and a Theorem of Jacquet-Martin
• On certain period relations for cusp forms on GL_n
• Comparison results for certain periods of cusp forms on GL(2n) over a totally real number field