The First Moment of L((1)/(2),χ) for Real Quadratic Function Fields

2019/08/12 by Andrade, J. C., MacMillan, J.
#11G20 #11M06 #11M38 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1908.04078

Abstract

In this paper we use techniques first introduced by Florea to improve the asymptotic formula for the first moment of the quadratic Dirichlet L-functions over the rational function field, running over all monic, square-free polynomials of even degree at the central point. With some extra technical difficulties that doesn't appear in Florea's paper, we prove that there are extra main terms of size (2g+2)q^(2g+2)/(3), q^{(g)/(6)+[(g)/(2)]} and q^{(g)/(6)+[(g-1)/(2)]}, whilst bounding the error term by q^{(g)/(2)(1+ε)}.

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