论文标题
各种积分点的多元正态分布
Multivariate normal distribution for integral points on varieties
论文作者
论文摘要
给定$ \ mathbb {q} $的品种，我们研究了将坐标数的数量分布，因为我们改变了一个不可或缺的点。 在合适的假设下，我们表明这具有多元正态分布。我们将其推广到更一般的魏尔除数，在那里我们获得了对协方差矩阵的几何解释。 为了我们的结果，我们开发了适用于相当通用整数序列的ERDőS-KAC定理的版本，不需要分布级的积极指数。
Given a variety over $\mathbb{Q}$, we study the distribution of the number of primes dividing the coordinates as we vary an integral point. Under suitable assumptions, we show that this has a multivariate normal distribution. We generalise this to more general Weil divisors, where we obtain a geometric interpretation of the covariance matrix. For our results we develop a version of the Erdős-Kac theorem that applies to fairly general integer sequences and does not require a positive exponent of level of distribution.
