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Distribution properties of generalized polynomials

  • Manfred G. Madritsch
  • Robert F. Tichy
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@misc{madritsch2026distribution,
  title = {{Distribution properties of generalized polynomials}},
  author = {Manfred G. Madritsch and Robert F. Tichy},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.04986},
  eprint = {2609.04986},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.04986},
}
RIS
TY  - UNPB
TI  - Distribution properties of generalized polynomials
AU  - Manfred G. Madritsch
AU  - Robert F. Tichy
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.04986
UR  - https://arxiv.org/abs/2609.04986
AB  - 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.
ER  -