2014/01/02 by Julio C. Andrade, Jonathan P. Keating · 1 citation
Mathematics · #math.NT #msc:11M38 #msc:11M50
published as Acta Arithmetica - Acta Arith. Volume 161, Number 4 (2013), 371-385 · 17 pages
arxiv created 2014/01/02 · arxiv updated 2014/01/03
The first and second moments are established for the family of quadratic Dirichlet L--functions over the rational function field at the central point s=\tfrac12 where the character χ is defined by the Legendre symbol for polynomials over finite fields and runs over all monic irreducible polynomials P of a given odd degree. Asymptotic formulae are derived for fixed finite fields when the degree of P is large. The first moment obtained here is the function field analogue of a result due to Jutila in the number--field setting. The approach is based on classical analytical methods and relies on the use of the analogue of the approximate functional equation for these L--functions.