On the distribution of class numbers of real quadratic function fields of Chowla type
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Let $k = \mathbb{F}_{q}(t)$ be a rational function field over the finite field $\mathbb{F}_{q}$, where $q$ is odd. In this paper we investigate the distribution of class numbers in the family of real quadratic function fields $k(\sqrt{D})$ of Chowla type over $k$. The strategy of this paper is to compare the distribution of $L(1,\chi_{D})$ to that of a random Euler product $L(1,\mathbb{X})$, which is a function field analogue of the one by Dahl and Lamzouri.
Abstract
Let $k = \mathbb{F}_{q}(t)$ be a rational function field over the finite field $\mathbb{F}_{q}$, where $q$ is odd. In this paper we investigate the distribution of class numbers in the family of real quadratic function fields $k(\sqrt{D})$ of Chowla type over $k$. The strategy of this paper is to compare the distribution of $L(1,\chi_{D})$ to that of a random Euler product $L(1,\mathbb{X})$, which is a function field analogue of the one by Dahl and Lamzouri.