Measurement of the branching fraction of <i>D_s</i><SUP>+</SUP> → <i>l</i><SUP>+</SUP>ν<i>_l</i> via <i>e</i><SUP>+</SUP><i>e</i><SUP>-</SUP> → <i>D_s</i>*<SUP>+</SUP><i>D_s</i>*<SUP>-</SUP>

Based on 10.64 fb(-1) of ethorne- collision data taken at center-of-mass energies between 4.237 and 4.699 GeV with the BESIII detector, we study the leptonic D-s(+) decays using the e(+)e(-) -> D-sD-+(s)(-) process. The branching fractions of D-s(+) -> l(+)nu(l)(l = mu, tau) are measured to be BDs+ -> mu+nu mu = (0.547 +/- 0.026(stat) +/- 0.016(syst))% and BDs+ ->tau+nu tau = (5.60 +/- 0.16(stat) +/- 0.20s(yst))%, respectively. The product of the decay constant and CabibboKobayashi-Maskawa matrix element vertical bar V-cs vertical bar is determined to be f(Ds+)vertical bar V-cs vertical bar = (246.5 +/- 5.9(stat) +/- 3.6(syst) +/- 0.5(input))(mu nu) and f(Ds+)vertical bar V-cs vertical bar = 252.7 +/- 3.6(stat) +/- 4.5(syst) +/- 0.6(input))(tau nu) MeV, respectively. Taking the value of vertical bar V-cs vertical bar from a global fit in the Standard Model, we obtain f(Ds+) = (253.2 +/- 6.0(stat) +/- 3.7(syst) +/- 0.6(input))(mu nu) and f(Ds+) = (259.6 +/- 3.7(stat) +/- 4.6(syst) +/- 0.6(input))(tau nu) MeV, respectively. Conversely, taking the value for f(Ds+) from the latest lattice quantum chromodynamics calculation, we obtain vertical bar V-cs vertical bar= (0.986 +/- 0.023(stat) +/- 0.014(syst) +/- 0.003(input))(mu nu) and vertical bar V-cs vertical bar = (1.011 +/- 0.014(stat) +/- 0.018(syst) +/- 0.003(input))(tau nu), respectively.