On a generalization of the Beiter Conjecture

Bartłomiej Bzdęga. "On a generalization of the Beiter Conjecture." Acta Arithmetica 173.2 (2016): 133-140. <http://eudml.org/doc/279437>.

@article{BartłomiejBzdęga2016,
abstract = {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₊.},
author = {Bartłomiej Bzdęga},
journal = {Acta Arithmetica},
keywords = {cyclotomic polynomial; coefficient; height of a polynomial},
language = {eng},
number = {2},
pages = {133-140},
title = {On a generalization of the Beiter Conjecture},
url = {http://eudml.org/doc/279437},
volume = {173},
year = {2016},
}

TY - JOUR
AU - Bartłomiej Bzdęga
TI - On a generalization of the Beiter Conjecture
JO - Acta Arithmetica
PY - 2016
VL - 173
IS - 2
SP - 133
EP - 140
AB - 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₊.
LA - eng
KW - cyclotomic polynomial; coefficient; height of a polynomial
UR - http://eudml.org/doc/279437
ER -