REMARK ON THE MEAN VALUE OF L( 1 IN THE HYPERELLIPTIC ENSEMBLE 2 , χ)

Abstract

Let A = Fq[T ] be a polynomial ring over Fq. In this paper we determine an asymptotic mean value of quadratic Dirichlet L-functions L(s, χγD) at the central point s = 1 2 , where D runs over all monic square-free polynomials of even degree in A and γ is a generator of F∗ q .

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