On triple product L-functions

2019/12/03 by Jayce R. Getz, Getz, Jayce R.
Mathematics · #11F66 #11F70 #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1912.01405

openalex publication_date 2019/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let π=π₁ ⊗ π₂ ⊗ π₃ be a unitary cuspidal automorphic representation of GL₃³(\mathbbA_F) where F is a number field. Assume that π is everywhere tempered. Under suitable local hypotheses, for a sufficiently large finite set of places S of F we prove that the triple product L-function L^S(s,π,⊗³) admits a meromorphic continuation to Re(s) >\tfrac12. We also give some information about the possible poles.

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