On Arithmetic Progressions of Powers in Cyclotomic Polynomials

Hung Viet Chu

On Arithmetic Progressions of Powers in Cyclotomic Polynomials

Number Theory 2021-06-07 v2

Authors: Hung Viet Chu

Abstract

We determine necessary conditions for when powers corresponding to positive/negative coefficients of $\Phi_{n}$ are in arithmetic progression. When $n = pq$ for any primes $q>p>2$ , our conditions are also sufficient. Finally, we generalize the result when $n = pq$ to the so-called inclusion-exclusion polynomials first introduced by Bachman.

Keywords

polynomials over finite fields polynomial theory positive polynomials

Cite

@article{arxiv.2001.08065,
  title  = {On Arithmetic Progressions of Powers in Cyclotomic Polynomials},
  author = {Hung Viet Chu},
  journal= {arXiv preprint arXiv:2001.08065},
  year   = {2021}
}

Comments

6 pages. Generalized the result when $n = pq$ to the so-called inclusion-exclusion polynomials first introduced by Bachman

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