On a generalization of the Beiter Conjecture

• Autorzy: Bartłomiej Bzdęga
• Języki publikacji: EN

Abstrakty

EN

We prove that for every ε > 0 and every nonnegative integer w there exist primes $p_1,...,p_w$ such that for $n = p_1... p_w$ the height of the cyclotomic polynomial $Φ_n$ is at least $(1-ε) c_w M_n$, where $M_n = ∏_{i=1}^{w-2} p_i^{2^{w-1-i}-1}$ and $c_w$ is a constant depending only on w; furthermore $lim_{w→∞} c_w^{2^{-w}} ≈ 0.71$. In our construction we can have $p_i > h(p_1... p_{i-1})$ for all i = 1,...,w and any function h: ℝ₊ → ℝ₊.

Kategorie tematyczne

• 11B83: Special sequences and polynomials
• 11C08: Polynomials

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2016
• Tom: 173
• Numer: 2
• Strony: 133-140

Daty

wydano

2016

Twórcy

autor

Bartłomiej Bzdęga

• Faculty of Mathematics and Computer Sciences, Adam Mickiewicz University, 61-614 Poznań, Poland

Identyfikatory

DOI

10.4064/aa8119-1-2016