Jumps of ternary cyclotomic coefficients

Bartłomiej Bzdęga

Acta Arithmetica, Tome 166 (2014), p. 203-213 / Harvested from The Polish Digital Mathematics Library

Résumé

It is known that two consecutive coefficients of a ternary cyclotomic polynomial $Φ_{p q r} (x) = \sum_{k} a_{p q r} (k) x^{k}$ differ by at most one. We characterize all k such that $| a_{p q r} (k) - a_{p q r} (k - 1) | = 1$ . We use this to prove that the number of nonzero coefficients of the nth ternary cyclotomic polynomial is greater than $n^{1 / 3}$ .

Publié le : 2014-01-01

Zbl 1307.11032

EUDML-ID : urn:eudml:doc:279067

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     author = {Bart\l omiej Bzd\k ega},
     title = {Jumps of ternary cyclotomic coefficients},
     journal = {Acta Arithmetica},
     volume = {166},
     year = {2014},
     pages = {203-213},
     zbl = {1307.11032},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa163-3-2}
}

Bartłomiej Bzdęga. Jumps of ternary cyclotomic coefficients. Acta Arithmetica, Tome 166 (2014) pp. 203-213. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa163-3-2/