The mean-square of Dirichlet L-functions

2007/08/20 by J. Brian Conrey, Conrey, J. Brian
Mathematics · #11M06 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11M06

paper · pdf · doi:10.48550/arxiv.0708.2699

arxiv created 2007/08/20 · arxiv updated 2009/12/01

Abstract

We verify the conjecture of [CFKRS] for the mean square near the critical point of Dirichlet L-functions for a composite modulus q. We also prove a kind of reciprocity formula when the second moment for a prime modulus is twisted by a character evaluated at a different prime.

Related

• Twisted fourth moment of Dirichlet L-functions to a fixed modulus
• Bounds for Moments of Dirichlet L-functions of fixed modulus on the critical line
• A Note on Twisted Moments of Dirichlet L-functions
• On twisted period functions and Moments of a weighted mean square of Dirichlet L-functions on the critical line
• The fourth moment of Dirichlet L-functions along the critical line