Spectral reciprocity via integral representations

Nunes, Ramon M.

doi:10.2140/ant.2023.17.1381

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Spectral reciprocity via integral representations

Ramon M. Nunes

Vol. 17 (2023), No. 8, 1381–1409

DOI: 10.2140/ant.2023.17.1381

Abstract

We prove a spectral reciprocity formula for automorphic forms on $GL (2)$ over a number field that is reminiscent of one found by Blomer and Khan. Our approach uses period representations of $L$ -functions and the language of automorphic representations.

Keywords

automorphic representations, L-functions, Rankin–Selberg

Mathematical Subject Classification

Primary: 11F03, 11F66, 11F70

Milestones

Received: 21 March 2021

Revised: 2 May 2022

Accepted: 6 July 2022

Published: 29 August 2023

Authors

Ramon M. Nunes
Departamento de Matemática Universidade Federal do Ceará Fortaleza Brazil

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Vol. 17, No. 8, 2023