论文标题
沿着耐力场的功能沿尼尔曼佛派的均匀分布
Uniform distribution in nilmanifolds along functions from a Hardy field
论文作者
论文摘要
我们研究了尼尔曼福尔德的平等分布性能，沿着耐力领域的多项式生长功能。更确切地说，如果$ x = g/γ$是nilmanifold，$ a_1，\ ldots，a_k \ in g $是通勤的nilrotations，而$ f_1，\ ldots，f_k $是hardy领域的多项式增长的功能 $ \ bullet $序列的分布$ a_1^{f_1（n）} \ cdot \ ldots \ cdot a_k^{f_k（n）}γ$由其在最大因素上投影，从而将莱布曼的等距级别的poltynomials扩展到了多个函数范围，从而将其扩展到了范围。和 $ \ bullet $ $ a_1^{f_1（n）} \ cdot \ ldots \ cdot a_k^{f_k（n）}γ$始终是sub-nilmanifolds的有限结合，这扩展了Leibman和Frantzikinakis对此主题的一些有限的结合。
We study equidistribution properties of translations on nilmanifolds along functions of polynomial growth from a Hardy field. More precisely, if $X=G/Γ$ is a nilmanifold, $a_1,\ldots,a_k\in G$ are commuting nilrotations, and $f_1,\ldots,f_k$ are functions of polynomial growth from a Hardy field then we show that $\bullet$ the distribution of the sequence $a_1^{f_1(n)}\cdot\ldots\cdot a_k^{f_k(n)}Γ$ is governed by its projection onto the maximal factor torus, which extends Leibman's Equidistribution Criterion form polynomials to a much wider range of functions; and $\bullet$ the orbit closure of $a_1^{f_1(n)}\cdot\ldots\cdot a_k^{f_k(n)}Γ$ is always a finite union of sub-nilmanifolds, which extends some of the previous work of Leibman and Frantzikinakis on this topic.
