2020/07/15 by Martin Čech, Čech, Martin
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2007.07800
openalex publication_date 2020/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the double character sum ∑_\substackm≤ X, m\odd∑_\substackn≤ Y, n\odd\leg mn and its smoothly weighted counterpart. An asymptotic formula with power saving error term was obtained by Conrey, Farmer and Soundararajan by applying the Poisson summation formula. The result is interesting, because the main term involves a non-smooth function. In this paper, we apply the inverse Mellin transform twice and study the resulting double integral that involves a double Dirichlet series. This method has two advantages -- it leads to a better error term, and the surprising main term naturally arises from three residues of the double Dirichlet series.