Spectral reciprocity via integral representations

Abstract

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

arXiv commentMany improvements throughout the text. Including the inclusion of a previously neglected main term

References in corpus (8)

• The subconvexity problem for $\GL_{2}$
• The second moment of twisted modular L-functions
• Burgess-like subconvex bounds for $G{L}_2\times G{L}_1$
• Twisted moments of L-functions and spectral reciprocity
• Level Reciprocity in the twisted second moment of Rankin-Selberg L-functions
• Motohashi's fourth moment identity for non-archimedean test functions and applications
• Simultaneous non-vanishing of $GL(3)\times GL(2)$ and GL(2) $L$-functions
• Periods and Reciprocity II

Cited by in corpus (6)

• Spectral Moment Formulae for $GL(3)\times GL(2)$ $L$-functions III: The Twisted Case
• Motohashi's Formula for the Fourth Moment of Individual Dirichlet $L$-Functions and Applications
• Spectral Moment Formulae for $GL(3)\times GL(2)$ $L$-functions I: The Cuspidal Case
• Spectral Reciprocity for the product of Rankin-Selberg $L$-functions
• $L^p$-Norm Bounds for Automorphic Forms via Spectral Reciprocity
• Spectral Moment Formulae for $GL(3)\times GL(2)$ $L$-functions II: The Eisenstein Case