On the genericity of Eisenstein series and their residues for covers of GLm

Solomon Friedberg*, David Ginzburg

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Let τ1(r), τ2(r) be two genuine cuspidal automorphic representations on r-fold covers of the adelic points of the general linear groups GLn1, GLn2, respectively, and let E(g, s) be the associated Eisenstein series on an r-fold cover of GLn1+n2, normalized to have functional equation under s ⟼ 1 - s. Suppose R(s) ≥ 1/2 without loss. Then the value at any point of holomorphy s = s0 or the reside at any (simple) pole of E(g, s) is an automorphic form, and generates an automorphic representation. In this note we show that if n1 ≠ n2 these automorphic representations (when not identically zero) are generic, while if n1 = n2 := n they are generic except for residues at s = n+1/2n.

Original languageEnglish
Pages (from-to)1000-1012
Number of pages13
JournalInternational Mathematics Research Notices
Volume2017
Issue number4
DOIs
StatePublished - 2017

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