# Non-Beiter ternary cyclotomic polynomials with an optimally large set of coefficients

@inproceedings{Moree2012NonBeiterTC, title={Non-Beiter ternary cyclotomic polynomials with an optimally large set of coefficients}, author={Pieter Moree and Eugenia Rosu}, year={2012} }

Let l ≥ 1 be an arbitrary odd integer and p, q and r be primes. We show that there exist infinitely many ternary cyclotomic polynomials Φpqr(x) with l2 + 3l + 5 ≤ p < q < r such that the set of coefficients of each of them consists of the p integers in the interval [-(p - l - 2)/2, (p + l + 2)/2]. It is known that no larger coefficient range is possible. The Beiter conjecture states that the cyclotomic coefficients apqr(k) of Φpqr satisfy |apqr(k)| ≤ (p + 1)/2 and thus the above family… CONTINUE READING

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