Jumps of ternary cyclotomic coefficients
Acta Arithmetica, Tome 163 (2014) no. 3, pp. 203-213
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
It is known that two consecutive coefficients of a ternary cyclotomic polynomial $\varPhi _{pqr}(x)= \sum _k a_{pqr}(k)x^k$ 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 $n$th ternary cyclotomic polynomial is greater than $n^{1/3}$.
Keywords:
known consecutive coefficients ternary cyclotomic polynomial varphi pqr sum pqr differ characterize pqr a pqr k prove number nonzero coefficients nth ternary cyclotomic polynomial greater
Affiliations des auteurs :
Bartłomiej Bzdęga 1
@article{10_4064_aa163_3_2,
author = {Bart{\l}omiej Bzd\k{e}ga},
title = {Jumps of ternary cyclotomic coefficients},
journal = {Acta Arithmetica},
pages = {203--213},
year = {2014},
volume = {163},
number = {3},
doi = {10.4064/aa163-3-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa163-3-2/}
}
Bartłomiej Bzdęga. Jumps of ternary cyclotomic coefficients. Acta Arithmetica, Tome 163 (2014) no. 3, pp. 203-213. doi: 10.4064/aa163-3-2
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