Exclusive rho^0-meson electroproduction is studied in the HERMES experiment, using a 27.6 GeV longitudinally polarized electron/positron beam and unpolarized hydrogen and deuterium targets in the kinematic region 0.5 GeV^2 < Q^2 < 7.0 GeV^2, 3.0 GeV < W < 6.3 GeV, and -t < 0.4 GeV^2. Real and imaginary parts of the ratios of the natural-parity-exchange helicity amplitudes T_{11} (gamma^*_T --> rho_T), T_{01} (gamma^*_T --> rho_L), T_{10} (gamma^*_L --> rho_T), and T_{1-1} (gamma^*_{-T} -->rho_T) to T_{00} (gamma^*_L --> rho_L) are extracted from the data. For the unnatural-parity-exchange amplitude U_{11}, the ratio |U_{11}/T_{00}| is obtained. The Q^2 and t dependences of these ratios are presented and compared with perturbative QCD predictions.
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