6533b7d4fe1ef96bd1262028
RESEARCH PRODUCT
The maximal coefficient of ternary cyclotomic polynomials with one free prime
Dominik Dudasubject
Discrete mathematicsReciprocal polynomialPolynomialAlgebra and Number TheoryAbsolute value (algebra)Ternary operationCyclotomic polynomialPrime (order theory)Mathematicsdescription
A cyclotomic polynomial Φn(x) is said to be ternary if n = pqr, with p, q and r distinct odd primes. Let M(p, q) be the maximum (in absolute value) coefficient appearing in the polynomial family Φpqr(x) with p < q < r, p and q fixed. Here a stronger version of the main conjecture of Gallot, Moree and Wilms regarding M(p, q) is established. Furthermore it is shown that there is an algorithm to compute M(p): = max {M(p, q): q > p}. Our methods are the most geometric used so far in the study of ternary cyclotomic polynomials.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-05-21 |