  The spectral function and dynamic structure factor of bosons interacting by
contact repulsion and confined to one dimension exhibit power-law singularities
along the dispersion curves of the collective modes. We find the corresponding
exponents exactly, by relating them to the known Bethe ansatz solution of the
Lieb-Liniger model. The found exponents vary considerably with the interaction
strength and momentum. Remarkably, the Luttinger liquid theory predictions for
the exponents fail even at low energies, once the immediate vicinities of the
edges are considered.
