A dynamical system proof of Niven's theorem and its extensions

Chatchawan Panraksa; Detchat Samart; Songpon Sriwongsa

A dynamical system proof of Niven's theorem and its extensions

Number Theory 2023-04-18 v1 Dynamical Systems

Authors: Chatchawan Panraksa , Detchat Samart , Songpon Sriwongsa

Abstract

Niven's theorem asserts that $\{\cos(r\pi) \mid r\in \mathbb{Q}\}\cap \mathbb{Q}=\{0,\pm 1,\pm 1/2\}.$ In this paper, we use elementary techniques and results from arithmetic dynamics to obtain an algorithm for classifying all values in the set $\{\cos(r\pi) \mid r\in \mathbb{Q}\}\cap K$ , where $K$ is an arbitrary number field.

Keywords

niven's theorem arithmetic dynamics cosine values rational numbers number field classification algorithm

Cite

@article{arxiv.2304.07823,
  title  = {A dynamical system proof of Niven's theorem and its extensions},
  author = {Chatchawan Panraksa and Detchat Samart and Songpon Sriwongsa},
  journal= {arXiv preprint arXiv:2304.07823},
  year   = {2023}
}

Comments

13 pages, to appear in Bull. Aust. Math. Soc

A dynamical system proof of Niven's theorem and its extensions

Abstract

Keywords

Cite

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