Adelically summable normalized weights and adelic equidistribution of effective divisors having small diagonals and small heights on the Berkovich projective lines
Adelically summable normalized weights and adelic equidistribution of effective divisors having small diagonals and small heights on the Berkovich projective lines
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发表时间：
2016-09
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通讯作者：
Y. Okuyama
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作者：
Y. Okuyama
我们引入了一个adelically可和的归一化权重g的概念，这是一个家庭的规范化的Berkovich投影线满足可和性条件的权重。然后，我们建立了一个有效k-因子在乘积公式域k $的可分闭包k_s$ in $\overline{k}$上的投影线上的等距离分布，该乘积公式域k$具有小g$-高度和小对角线。这一等分布结果推广了叶的伽罗瓦共轭类的代数数关于拟adelic措施。
We introduce the notion of an adelically summable normalized weight $g$, which is a family of normalized weights on the Berkovich projective lines satisfying a summability condition. We then establish an adelic equidistribution of effective $k$-divisors on the projective line over the separable closure $k_s$ in $\overline{k}$ of a product formula field $k$ having small $g$-heights and small diagonals. This equidistribution result generalizes Ye's for the Galois conjugacy classes of algebraic numbers with respect to quasi-adelic measures.