[en] First-order Born cross sections for electron-positron pair production in relativistic heavy-ion collisions are calculated. Sommerfeld-Maue wave functions are employed to describe the continuum state of the emitted electron and positron in the field of the heavy target nucleus. Double-differential, single-differential, and total cross sections are presented in a wide energy regime from 1 GeV/u up to 20 TeV/u. We compare our results with first-Born calculations using a partial-wave expansion and with lowest-order QED calculations. The target-charge dependence is investigated