论文标题
功能字段的班级数量的矩和统计分布
The Moments and statistical Distribution of Class number of Primes over Function Fields
论文作者
论文摘要
我们调查了$ l（1，\ x_p）的时刻和分布，其中$ \ x_p $在与不可约多项式$ p $ p $ a $ 2g+1 $相关的二次字符上有所不同。在本文的第一部分中，我们计算了类Number $ H_ {P} $与二次函数字段相关的类的整体矩，具有Prime Indicnats $ p $，这是通过适应Nagoshi在数字字段设置的Nagoshi进行的一些先前结果来完成的。在本文的第二部分中，我们计算$ L（1，\ x_p）$的复杂矩在大统一范围内，并通过引入某个随机的Euler产品来研究类数字的统计分布。本文的第二部分是基于Lumley在处理无平方多项式时进行的最新结果。
We investigate the moment and the distribution of $L(1,\x_P),$ where $\x_P$ varies over quadratic characters associated to irreducible polynomials $P$ of degree $2g+1$ over $\mathbb{F}_q[T]$ as $g\to\infty$. In the first part of the paper we compute the integral moments of the class number $h_{P}$ associated to quadratic function fields with prime discriminants $P$ and this is done by adapting to the function field setting some of the previous results carried out by Nagoshi in the number field setting. In the second part of the paper we compute the complex moments of of $L(1,\x_P)$ in large uniform range and investigate the statistical distribution of the class numbers by introducing a certain random Euler product. The second part of the paper is based on recent results carried out by Lumley when dealing with square-free polynomials.
