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arXiv · 0712.2365

Ternary cyclotomic polynomials having a large coefficient

Yves Gallot·Pieter Moree
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Abstract

Let $Φ_n(x)$ denote the $n$th cyclotomic polynomial. In 1968 Sister Marion Beiter conjectured that $a_n(k)$, the coefficient of $x^k$ in $Φ_n(x)$, satisfies $|a_n(k)|\le (p+1)/2$ in case $n=pqr$ with $p 0$ there exist infinitely many triples $(p_j,q_j,r_j)$ with $p_1 (2/3-ε)p_j$ for $j\ge 1$.

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Yves Gallot, Pieter Moree. 2008-04-14. Ternary cyclotomic polynomials having a large coefficient. https://arxiv.org/abs/0712.2365

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