We report a new precise determination of the leptonic widths of the J/psi meson performed with the KEDR detector at the VEPP-4M $e^{+}e^{-}$ collider. The measured values of the J/psi parameters are: Gamma_{ee}timesGamma_{ee}/Gamma = 0.3323 pm 0.0064 (stat.) pm 0.0048 (syst.) keV Gamma_{ee}timesGamma_{mumu}/Gamma=0.3318 pm 0.0052 (stat.) pm 0.0063 (syst.) keV. Assuming $emu$ universality and using the table value of the branching ratios the leptonic Gamma_{ll}= 5.59 pm 0.12 keV width and the total Gamma=94.1 pm 2.7 keV widths were obtained. We also discuss in detail a method to calculate radiative corrections at a narrow resonance.
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