English

On Euler's totient function of polynomials over finite fields

Number Theory 2025-05-22 v2

Abstract

In this paper, we study some typical arithmetic properties of Euler's totient function of polynomials over finite fields. Especially, we study polynomial analogues of some classical conjectures about Euler's totient function, such as Carmichael's conjecture, Sierpi\'{n}ski's conjecture, and Erd\"{o}s' conjecture.

Keywords

Cite

@article{arxiv.2401.17727,
  title  = {On Euler's totient function of polynomials over finite fields},
  author = {Xiumei Li and Min Sha},
  journal= {arXiv preprint arXiv:2401.17727},
  year   = {2025}
}

Comments

19 pages

R2 v1 2026-06-28T14:32:53.846Z