Breaking the (1)/(2)-barrier for the twisted second moment of Dirichlet L-functions

2018/08/31 by Hung M. Bui, Bui, H. M., Kyle Pratt +5
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1808.10803

openalex publication_date 2018/08/31 · openalex created_date 2018/09/07 · openalex updated_date 2026/07/28

Abstract

We study the second moment of Dirichlet L-functions to a large prime modulus q twisted by the square of an arbitrary Dirichlet polynomial. We break the (1)/(2)-barrier in this problem, and obtain an asymptotic formula provided that the length of the Dirichlet polynomial is less than q^51/101 = q^{1/2 +1/202}. As an application, we obtain an upper bound of the correct order of magnitude for the third moment of Dirichlet L-functions. We give further results when the coefficients of the Dirichlet polynomial are more specialized.

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