REMARK ON THE MEAN VALUE OF L(½, χ) IN THE HYPERELLIPTIC ENSEMBLE
REMARK ON THE MEAN VALUE OF L(½, χ) IN THE HYPERELLIPTIC ENSEMBLE
Let <TEX>$\mathbb{A}=\mathbb{F}_q[T]$</TEX> be a polynomial ring over <TEX>$\mathbb{F}_q$</TEX>. In this paper we determine an asymptotic mean value of quadratic Dirich-let L-functions L(s, <TEX>${\chi}_{{\gamma}D}$</TEX>) at the central point s=<TEX>$\frac{1}{2}$</TEX>, where D runs over all monic square-free polynomials of even degree in <TEX>$\mathbb{A}$</TEX> and <TEX>${\gamma}$</TEX> is a generator of <TEX>$\mathbb{F}_q^*$</TEX>.