The moments of quadratic Dirichlet L-functions over function fields have recently attracted much attention with the work of Andrade and Keating. In this article, we establish lower bounds for the mean values of the product of quadratic Dirichlet L-functions associated with hyperelliptic curves of genus g over a fixed finite field ${\mathbb{F}}_q$ in the large genus limit. By using the idea of A. Florea [14], we also obtain their upper bounds. As a consequence, we find upper bounds of its derivatives. These lower and upper bounds give the correlation of quadratic Dirichlet L-functions associated with hyperelliptic curves with different transitions.

中文翻译：

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超椭圆系综中 L 函数位移值的相关性

函数场上二次狄利克雷L函数的矩最近随着 Andrade 和 Keating 的工作引起了很多关注。在本文中，我们建立了与g属的超椭圆曲线在固定有限域上的二次狄利克雷L函数乘积的平均值的下界${\mathbb{F}}_q$在大属极限。通过使用 A. Florea [14] 的思想，我们也得到了它们的上界。因此，我们找到了其导数的上限。这些下限和上限给出了与具有不同跃迁的超椭圆曲线相关的二次狄利克雷L函数的相关性。