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Test vectors for non‐Archimedean Godement–Jacquet zeta integrals

Humphries, P; (2021) Test vectors for non‐Archimedean Godement–Jacquet zeta integrals. Bulletin of the London Mathematical Society , 53 (1) pp. 92-99. 10.1112/blms.12401. Green open access

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Abstract

Given an induced representation of Langlands type ( π , V π ) of GL n ( F ) with F non‐Archimedean, we show that there exist explicit choices of matrix coefficient β and Schwartz–Bruhat function Φ for which the Godement–Jacquet zeta integral Z ( s , β , Φ ) attains the L ‐function L ( s , π ).

Type: Article
Title: Test vectors for non‐Archimedean Godement–Jacquet zeta integrals
Open access status: An open access version is available from UCL Discovery
DOI: 10.1112/blms.12401
Publisher version: https://doi.org/10.1112/blms.12401
Language: English
Additional information: © 2020 The Authors. Bulletin of the London Mathematical Society is copyright © London Mathematical Society. This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial‐NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non‐commercial and no modifications or adaptations are made.
Keywords: 11F70 (primary), 20G05, 22E50 (secondary)
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
URI: https://discovery.ucl.ac.uk/id/eprint/10126861
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