  A knot in the 3-sphere is called an L-space knot if it admits a nontrivial
Dehn surgery yielding an L-space, i.e. a rational homology 3-sphere with the
smallest possible Heegaard Floer homology. Given a knot K, take an unknotted
circle c and twist K n times along c to obtain a twist family { K_n }. We give
a sufficient condition for { K_n } to contain infinitely many L-space knots. As
an application we show that for each torus knot and each hyperbolic Berge knot
K, we can take c so that the twist family { K_n } contains infinitely many
hyperbolic L-space knots. We also demonstrate that there is a twist family of
hyperbolic L-space knots each member of which has tunnel number greater than
one.
