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Jumps of ternary cyclotomic coefficients

Number Theory 2014-07-15 v1

Abstract

It is known that two consecutive coefficients of a ternary cyclotomic polynomial Φpqr(x)=kapqr(k)xk\Phi_{pqr}(x)=\sum_k a_{pqr}(k)x^k differ by at most one. In this paper we give a criterion on kk to satisfy apqr(k)apqr(k1)=1|a_{pqr}(k)-a_{pqr}(k-1)|=1. We use this to prove that the number of nonzero coefficients of the nnth ternary cyclotomic polynomial is greater than n1/3n^{1/3}.

Keywords

Cite

@article{arxiv.1301.7174,
  title  = {Jumps of ternary cyclotomic coefficients},
  author = {Bartlomiej Bzdega},
  journal= {arXiv preprint arXiv:1301.7174},
  year   = {2014}
}

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10 pages