Twisted moments of L-functions and spectral reciprocity

Abstract

A reciprocity formula is established that expresses the fourth moment of automorphic L-functions of level q twisted by the ell-th Hecke eigenvalue as the fourth moment of automorphic L-functions of level ell twisted by the q-th Hecke eigenvalue. Direct corollaries include subconvexity bounds for L-functions in the level aspect and a short proof of an upper bound for the fifth moment of automorphic L-functions.

42 pages, minor errors in the first version corrected

References in corpus (3)

• The second moment of twisted modular L-functions
• On the reciprocity law for the twisted second moment of Dirichlet $L$-functions
• A Functional Equation for the Spectral Fourth Moment of Modular Hecke L-Functions

Cited by in corpus (12)

• The fourth moment of Dirichlet $L$-functions along a coset and the Weyl bound
• Motohashi's fourth moment identity for non-archimedean test functions and applications
• On the Random Wave Conjecture for Dihedral Maaß Forms
• Spectral reciprocity via integral representations
• 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 III: The Twisted Case
• Mixed moment of $GL(2)$ and $GL(3)$ $L$-functions
• Spectral Moment Formulae for $GL(3)\times GL(2)$ $L$-functions I: The Cuspidal Case
• $L^p$-Norm Bounds for Automorphic Forms via Spectral Reciprocity
• Mixed Moments of the Riemann Zeta and Dirichlet $L$-Functions
• Strong Hybrid Subconvexity for Twisted Selfdual ${\mathrm{GL}}_3$ $L$-Functions
• On the balanced Voronoi formula for GL${}_N$