Geodesic
Jumps of ternary cyclotomic coefficients
Bartłomiej Bzdęga1
1 Faculty of Mathematics and Computer Science Adam Mickiewicz University Umultowska 87 61-614 Poznań, Poland
Acta Arithmetica, Tome 163 (2014) no. 3, pp. 203-213.

Voir la notice de l'article provenant de 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 $n^{1/3}$.
DOI : 10.4064/aa163-3-2
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

Bartłomiej Bzdęga 1

1 Faculty of Mathematics and Computer Science Adam Mickiewicz University Umultowska 87 61-614 Poznań, Poland 
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Bartłomiej Bzdęga. Jumps of ternary cyclotomic coefficients. Acta Arithmetica, Tome 163 (2014) no. 3, pp. 203-213. doi : 10.4064/aa163-3-2. http://geodesic.mathdoc.fr/articles/10.4064/aa163-3-2/

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