Radiative Corrections to the decay tau -> pi (K) nu_tau

We have calculated the O(alpha) radiative corrections to the tau decay tau -> pi (K) nu, taking into account both the point meson contribution and the structure dependent radiation. We find for the ratio Gamma(tau -> pi nu (gamma)) / Gamma(pi -> mu nu (gamma)) a radiative correction of + 1.2% and for Gamma(tau -> K nu (gamma)) / Gamma(K -> mu nu (gamma)) one of + 2.0%. We compare our results with an earlier estimation and with experimental data.