Ternary cyclotomic polynomials having a large coefficient

Details Ternary cyclotomic polynomials having a large coefficient Ternary cyclotomic polynomials having a large coefficient

2007-12-14

arxiv.org/abs/0712.2365v2

Mathematics

Number Theory

19 pages, 6 tables, to appear in Crelle's Journal. Revised version with many small changes

Scientific paper

Let $\Phi_n(x)$ denote the $n$th cyclotomic polynomial. In 1968 Sister Marion Beiter conjectured that $a_n(k)$, the coefficient of $x^k$ in $\Phi_n(x)$, satisfies $|a_n(k)|\le (p+1)/2$ in case $n=pqr$ with $p0$ there exist infinitely many triples $(p_j,q_j,r_j)$ with $p_1(2/3-\epsilon)p_j$ for $j\ge 1$.

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