Uniform bounds on $S$-integral preperiodic points for chebyshev polynomials

Rudranarayan Padhy; Sudhansu Sekhar Rout

Uniform bounds on $S$-integral preperiodic points for chebyshev polynomials

Number Theory 2024-10-03 v1

Authors: Rudranarayan Padhy , Sudhansu Sekhar Rout

Abstract

Let $K$ be a number field with algebraic closure $\bar{K}$ , let $S$ be a finite set of places of $K$ containing the archimedean places, and let $\varphi$ be Chebyshev polynomial. In this paper we prove uniformity results on the number of $S$ -integral preperiodic points relative to a non-preperiodic point $\beta$ , as $\beta$ varies over number fields of bounded degree.

Cite

@article{arxiv.2410.00937,
  title  = {Uniform bounds on $S$-integral preperiodic points for chebyshev polynomials},
  author = {Rudranarayan Padhy and Sudhansu Sekhar Rout},
  journal= {arXiv preprint arXiv:2410.00937},
  year   = {2024}
}

Comments

14 pages. arXiv admin note: text overlap with arXiv:2302.01562, arXiv:0808.2679, arXiv:0805.1554 by other authors

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