  Given a numerical semigroup $S$, we let $\mathrm P_S(x)=(1-x)\sum_{s\in
S}x^s$ be its semigroup polynomial. We study cyclotomic numerical semigroups;
these are numerical semigroups $S$ such that $\mathrm P_S(x)$ has all its roots
in the unit disc. We conjecture that $S$ is a cyclotomic numerical semigroup if
and only if $S$ is a complete intersection numerical semigroup and present some
evidence for it. Aside from the notion of cyclotomic numerical semigroup we
introduce the notion of cyclotomic exponents and polynomially related numerical
semigroups. We derive some properties and give some applications of these new
concepts.
