Jumps of ternary cyclotomic coefficients

Bartłomiej Bzdęga. "Jumps of ternary cyclotomic coefficients." Acta Arithmetica 163.3 (2014): 203-213. <http://eudml.org/doc/279067>.

@article{BartłomiejBzdęga2014,
abstract = {It is known that two consecutive coefficients of a ternary cyclotomic polynomial $Φ_\{pqr\}(x)= ∑_k a_\{pqr\}(k)x^k$ differ by at most one. We characterize all k such that $|a_\{pqr\}(k)-a_\{pqr\}(k-1)|=1$. We use this to prove that the number of nonzero coefficients of the nth ternary cyclotomic polynomial is greater than $n^\{1/3\}$.},
author = {Bartłomiej Bzdęga},
journal = {Acta Arithmetica},
keywords = {ternary cyclotomic polynomials; ternary inclusion-exclusion polynomials},
language = {eng},
number = {3},
pages = {203-213},
title = {Jumps of ternary cyclotomic coefficients},
url = {http://eudml.org/doc/279067},
volume = {163},
year = {2014},
}

TY - JOUR
AU - Bartłomiej Bzdęga
TI - Jumps of ternary cyclotomic coefficients
JO - Acta Arithmetica
PY - 2014
VL - 163
IS - 3
SP - 203
EP - 213
AB - It is known that two consecutive coefficients of a ternary cyclotomic polynomial $Φ_{pqr}(x)= ∑_k a_{pqr}(k)x^k$ differ by at most one. We characterize all k such that $|a_{pqr}(k)-a_{pqr}(k-1)|=1$. We use this to prove that the number of nonzero coefficients of the nth ternary cyclotomic polynomial is greater than $n^{1/3}$.
LA - eng
KW - ternary cyclotomic polynomials; ternary inclusion-exclusion polynomials
UR - http://eudml.org/doc/279067
ER -