Prompt-photon production in deep inelastic scattering at HERA ZEUS Collaboration Prompt-photon cross sections in deep inelastic ep scattering were measured with the ZEUS detector at HERA using an integrated luminosity of 320 pb-1. A clear signal for isolated photons in the photon transverse-energy and rapidity ranges 4 < E_T^gamma < 15 GeV and -0.7 < eta^gamma < 0.9 was observed for virtualities of the exchanged photon of Q^2 > 10 GeV^2. Measurements of differential cross sections are presented for inclusive prompt-photon production as a function of Q^2, x_Bj, E_T^gamma and eta^gamma. Perturbative QCD predictions are compared to the measurements.