The first moment of cusp form L-functions in weight aspect on average

2017/03/02 by Balkanova, Olga, Frolenkov, Dmitry
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1703.00742

Abstract

We study the asymptotic behaviour of the twisted first moment of central L-values associated to cusp forms in weight aspect on average. Our estimate of the error term allows extending the logarithmic length of mollifier Δ up to 2. The best previously known result, due to Iwaniec and Sarnak, was Δ<1. The proof is based on a representation formula for the error in terms of Legendre polynomials.

Related

• On mean values of mollifiers and L-functions associated to primitive\n cusp forms
• Averages of long Dirichlet polynomials with modular coefficients
• The second moment theory of families of L-functions
• Short Second Moment Bound for GL(2) L-functions in q-Aspect
• The first moment of Maass form symmetric square L-functions