  We calculate the form factors of the $K \to \pi l \nu$ semileptonic decays in
three-flavor lattice QCD, and study their chiral behavior as a function of the
momentum transfer and the Nambu-Goldstone boson masses. Chiral symmetry is
exactly preserved by using the overlap quark action, which enables us to
directly compare the lattice data with chiral perturbation theory (ChPT). We
generate gauge ensembles at a lattice spacing of 0.11fm with four pion masses
covering 290-540 MeV and a strange quark mass m_s close to its physical value.
By using the all-to-all quark propagator, we calculate the vector and scalar
form factors with high precision. Their dependence on m_s and the momentum
transfer is studied by using the reweighting technique and the twisted boundary
conditions for the quark fields. We compare the results for the semileptonic
form factors with ChPT at next-to-next-to leading order in detail. While many
low-energy constants appear at this order, we make use of our data of the light
meson electromagnetic form factors in order to control the chiral
extrapolation. We determine the normalization of the form factors as f_+(0) =
0.9636(36)(+57/-35), and observe reasonable agreement of their shape with
experiment.
