Hybrid Euler-Hadamard product for quadratic Dirichlet L-functions in function fields

2016/09/17 by H. M. Bui, Alexandra Florea
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Dirichlet distribution #Dirichlet problem #Function (biology) #Function field #Product (mathematics) #Quadratic equation #Quadratic function #math.NT

paper · pdf · doi:10.1112/plms.12123

arxiv created 2016/09/17 · openalex created_date 2016/09/30 · openalex publication_date 2018/03/28 · arxiv updated 2018/04/04 · openalex updated_date 2026/08/05

Abstract

We develop a hybrid Euler-Hadamard product model for quadratic Dirichlet L–functions over function fields (following the model introduced by Gonek, Hughes and Keating for the Riemann-zeta function). After computing the first three twisted moments in this family of L–functions, we provide further evidence for the conjectural asymptotic formulas for the moments of the family.

Citations

• The expression of a polynomial as a sum of three irreducibles
• Eisenstein series of 1/2-integral weight and the mean value of real DirichletL-series
• Conjectures for the integral moments and ratios of L-functions over function fields
• Random Matrix Theory and ζ(1/2+ it)
• Integral moments of L-functions
• Nonvanishing of Quadratic Dirichlet L-Functions at S = &#189