The Kronecker-Weyl equidistribution theorem and geodesics in 3-manifolds

次凸$L^p$集、Weyl不等式与等分布

Subconvex $L^p$-sets, Weyl's inequality, and equidistribution

本文研究满足次凸$L^p$界的自然数集，证明其上指数和满足类Weyl不等式且强度常与经典界相当，还探讨了相关多项式模1等分布及在特征和、算术函数平均值中的应用。

函数域中多项式序列的等分布及其应用

Equidistribution of polynomial sequences in function fields, with applications

本文证明了外尔多项式序列等分布定理在函数域中的类比，突破多项式次数不低于域特征这一差分法障碍，并应用于 van der Corput 集、相交集与 Glasner 集的研究。

幂零流的等分布与Weyl和的界

Equidistribution of nilflows and bounds on Weyl sums

该研究证明了丝状幂零流的有效等分布结果，推导了高次多项式Weyl和的界，其幂节省量与Vinogradov主猜想证明中的已知最优结果相当，论证结合了动力系统思想与非阿贝尔调和分析。

Drinfeld 的 Duke 定理

Duke for Drinfeld

本文在 Drinfeld–Stuhler 模曲线背景下证明了 CM 点的 Duke 均衡分布定理的函数域类比，将 Duke 定理和 Zhang 的均衡分布推广到 Drinfeld 情形，并处理了任意水平结构和正特征。

A Kronecker-Weyl theorem for subsets of abelian groups

Let N be the set of non-negative integer numbers, T the circle group and c the cardinality of the continuum. Given an abelian group G of size at most 2^c and a countable family F of infinite subsets of G, we construct "Baire many" monomorphisms p: G --> T^c such that p(E) is dense in {y in T^c : ny=0} whenever n in N, E in F, nE={0} and {x in E: mx=g} is finite for all g in G and m such that n=mk for some k in N--{1}. We apply this result to obtain an algebraic description of countable potentially dense subsets of abelian groups, thereby making a significant progress towards a solution of a pr…

Equidistribution, Uniform distribution: a probabilist's perspective

The theory of equidistribution is about hundred years old, and has been developed primarily by number theorists and theoretical computer scientists. A motivated uninitiated peer could encounter difficulties perusing the literature, due to various synonyms and polysemes used by different schools. One purpose of this note is to provide a short introduction for probabilists. We proceed by recalling a perspective originating in a work of the second author from 2002. Using it, various new examples of completely uniformly distributed (mod 1) sequences, in the "metric" (meaning almost sure stochastic…

用于分形上有效等分布与加权Khintchine–Schmidt定理的锥提升

Cone upgrade for effective equidistribution and weighted Khintchine--Schmidt theorem on fractals

该研究针对实线上具有共同压缩比的自相似测度乘积，证明了加权Khintchine-Schmidt定理的分形类似结果，通过提出锥提升方法，得到Khalil等人定理的部分有效形式。

关于由LCA群驱动的数论逼近的Weyl型定理及应用

A Weyl-type theorem for Diophantine approximations driven by LCA groups and applications

本文研究了LCA群在环面上的作用，提出了一种Weyl型等分布定理，证明了每个作用可分解为唯一ergodic子系统，并应用该结果得到LCA群的若干基础结论。

非可积三维流形中测地流的一致性

Uniformity of geodesic flow in non-integrable 3-manifolds

本文研究非可积有限多立方体平移三维流形上测地流的均匀分布问题，提出分裂方法处理含一个可积方向的笛卡尔积情形，并结合分裂覆盖论证将结果推广到三个方向均不可积且满足特殊条件的流形。

多项式扩展的莱米定理

Polynomial extensions of Raimi's theorem

本文研究了多项式扩展的莱米定理，证明在任意维度下多项式移位下交集性质保持，并探讨了有限群中的类似结果。