Non vanishing of products of twisted GL(3) L-functions

2021/12/16 by Frot, Robin
#11M06 #11M41 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2112.08927

Abstract

In this paper, we prove that if the Fourier coefficients of a SL(3,ℤ) Hecke--Maaß cusp form π are not too correlated with additive characters, then there exists infinitely many Dirichlet characters such that L((1)/(2),π⊗χ)L((1)/(2),χ)≠ 0. To prove this result, we compute the first twisted moment of these L function averaged over a well chosen set of conductors.

Related

• A zero-density estimate for L-functions associated with \rm GL(3) Hecke--Maass cusp forms
• Determination of \textrmGL(3) cusp forms by central values of quadratic twisted L-functions
• Additive twists of Fourier coefficients of GL(3) Maass forms
• Bounds for twists of \rm GL(3) L-functions
• Simultaneous nonvanishing of Dirichlet L-functions and twists of Hecke-Maass L-functions