Cyclotomic ordering conjecture

2019/03/06 by Glasby, S. P.
#11A07 #11C06 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1903.02951

Abstract

This note describes a conjecture involving cyclotomic polynomials and some initial thoughts towards a solution. Given positive integers m,n, the conjecture is that either Φ_m(q)\leqslantΦ_n(q) or Φ_m(q)\geqslantΦ_n(q) holds for all integers q\geqslant 2. Pomerance and Rubinstein-Salzedo proved the conjecture in a preprint called `Cyclotomic coincidences' [arXiv:1903.01962].

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