Maximal height of divisors of $x^{pq^{b}}-1$

Shaozu Wang

Maximal height of divisors of $x^{pq^{b}}-1$

Number Theory 2014-01-13 v2

Authors: Shaozu Wang

Abstract

The height of a polynomial $f(x)$ is the largest coefficient of $f(x)$ in absolute value. Let B(n) be the largest height of a polynomial in $\mathbb{Z}[x]$ dividing $x^n-1$ . In this paper we investigate the maximal height of divisors of $x^{pq^b}-1$ and prove that some conjectures on the maximal height of divisors of $x^{pq^b}-1$ are true.

Keywords

polynomial height cyclotomic polynomials divisors coefficients integer polynomials

Cite

@article{arxiv.1312.3108,
  title  = {Maximal height of divisors of $x^{pq^{b}}-1$},
  author = {Shaozu Wang},
  journal= {arXiv preprint arXiv:1312.3108},
  year   = {2014}
}

Comments

14 pages

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