An L-space is a 3-manifold whose Heegaard Floer homology is as
simple as possible. An L-space knot is a knot with a non-trivial L-space
surgery; examples are torus knots and Berge knots. Moore asked if the
double branched cover of a hyperbolic L-space knot is ever an L-space. We
show that if the n-fold cyclic branched cover of an (arbitrary) L-space
knot K is an L-space then  n < or = 5 ,  and obtain strong restrictions on
K when n = 3,4 or 5.

This is joint work with Michel Boileau and Steve Boyer.