English

On Salem numbers which are exceptional units

Number Theory 2023-09-28 v2

Abstract

By extending a construction due to Gross and McMullen [2], we show that for any odd integer n and for any even integer d>n+2 there are infinitely many Salem numbers α\alpha of degree d such that αn1\alpha^n-1 is a unit. A similar result is also proved when n runs through some classes of even integers, d>n+3 and d/2 is an odd integer.

Keywords

Cite

@article{arxiv.2309.07723,
  title  = {On Salem numbers which are exceptional units},
  author = {Toufik Zaimi},
  journal= {arXiv preprint arXiv:2309.07723},
  year   = {2023}
}
R2 v1 2026-06-28T12:21:34.993Z