发表机构
Technical University of Leoben; Graz University of Technology（列奥本工业大学; 格拉茨工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究广义多项式的分布性质，证明其渐近分布结果及沿素数的均匀分布结果并给出偏差界。
AI 中文摘要
广义多项式是由加法、乘法和下取整函数迭代定义的函数。Håland及后来Bergelson与Leibman从遍历理论角度建立了广义多项式序列的均匀分布结果。本文证明了可应用于某些广义多项式的渐近分布结果；第二部分还证明了沿素数的广义多项式的均匀分布结果，包括偏差的界。
英文摘要
A generalized polynomial is a function defined by an iteration of the operations addition, multiplication and the floor function. Equidistribution results of sequences given by generalized polynomials have been established by Håland and later by Bergelson and Leibman from an ergodic theoretic point of view. In the present paper we show an asymptotic distribution result which can be applied to certain generalized polynomials. In the second part we prove equidistribution results for generalized polynomials along prime numbers, including bounds for the discrepancy.
Comments20 pages
