The mean-square of Dirichlet L-functions

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.

Cited by in corpus (6)

• Surpassing the Ratios Conjecture in the 1-level density of Dirichlet $L$-functions
• The reciprocity law for the twisted second moment of Dirichlet L-functions
• Strong orthogonality between the Mobius function and nonlinear exponential functions in short intervals
• The sixth power moment of Dirichlet L-functions
• Periods and Reciprocity II
• A congruence sum and rational approximations