Fractional Moments of Dirichlet L-Functions

2009/10/12 by D. R. Heath‐Brown, D. R. Heath-Brown, Heath-Brown, D. R. · 3 citations
Mathematics · #11M06 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #math.NT #msc:11M06

paper · pdf · doi:10.48550/arxiv.0910.2102

arxiv created 2009/10/12 · openalex publication_date 2009/10/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k be a positive real number, and let M_k(q) be the sum of |L(\tfrac12,χ)|^2k over all non-principal characters to a given modulus q. We prove that M_k(q)≪_k ϕ(q)(log q)^k2 whenever k is the reciprocal n^-1 of a positive integer n. If one assumes the Generalized Riemann Hypothesis then the estimate holds for all positive real k<2.

Cited by

• A survey of moment bounds for ζ(s): from Heath Brown's work to the present
• Moments of Higher Logarithmic Derivatives and Exceptional Zeros in Cyclotomic Fields
• The hyperbolic circle problem over Heegner points

Related

• Bounds for moments of quadratic Dirichlet character sums of prime moduli
• Upper bounds for moments of Dirichlet L-functions to a fixed modulus
• On the twisted quadratic moment for Dirichlet L-functions
• A lower bound on high moments of character sums
• Estimates for character sums and Dirichlet L-functions to smooth moduli