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- W4299789683 abstract "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 $p<q<r$ primes (in this case $Phi_n(x)$ is said to be ternary). Since then several results towards establishing her conjecture have been proved (for example $|a_n(k)|le 3p/4$). Here we show that, nevertheless, Beiter's conjecture is false for every $pge 11$. We also prove that given any $epsilon>0$ there exist infinitely many triples $(p_j,q_j,r_j)$ with $p_1<p_2<... $ consecutive primes such that $|a_{p_jq_jr_j}(n_j)|>(2/3-epsilon)p_j$ for $jge 1$." @default.
- W4299789683 created "2022-10-03" @default.
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- W4299789683 date "2007-12-14" @default.
- W4299789683 modified "2023-09-30" @default.
- W4299789683 title "Ternary cyclotomic polynomials having a large coefficient" @default.
- W4299789683 doi "https://doi.org/10.48550/arxiv.0712.2365" @default.
- W4299789683 hasPublicationYear "2007" @default.
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