The maximum gap $g(f)$ of a polynomial $f$ is the maximum of the differences (gaps) between two consecutive exponents that appear in $f$. Let $\Phi_{ n}$ and $\Psi_{ n}$ denote the $n$-th cyclotomic and $n$-th inverse cyclotomic polynomial, respectively. In this paper, we give several lower bounds for $g(\Phi_{ n})$ and $g(\Psi_{ n})$, where $n$ is the product of odd primes. We observe that they are very often exact. We also give an exact expression for $g(\Psi_{ n})$ under a certain condition. Finally we conjecture an exact expression for $g(\Phi_{ n})$ under a certain condition.
Categories: math.NT