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Using data samples taken with the BES-III detector at the center-of-mass energies of √ s = 3.773 GeV, √ s = 4.009 GeV and √ s = 4.599 GeV, we studied leptonic, semileptonic and rare charm decays. From leptonic D+→ μνμ decays, we determined the most precise D+-meson decay constant fD+ =(203.2±5.3stat±1.8syst) MeV and the most precise Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix element |Vcd|= 0.2210±0.0058stat±0.0047syst. From the semileptonic D0 → K−e+ν and D0 → π−e+ν decays, we determined the most precise D-meson decay form factors f K + (0) = 0.7368± 0.0026stat ± 0.0036syst and f π +(0) = 0.6372± 0.0080stat ± 0.0044syst, as well as the CKM quark mixing matrix elements |Vcs| = 0.9601± 0.0058exp ± 0.0230LQCD and |Vcd| = 0.2155± 0.0030exp± 0.0094LQCD. These decay constant and form factors could be used to incisively validate Lattice QCD calculations of these quantities, in turn, to improve measurements of CP-violation in B decays. In addition, we measured the form factors for semileptonic D decays containing a vector meson in the final states, and searched for the rare D decays containing e+e− or e+e+ in the final state from the data taken at 3.773 GeV. Using the data taken at √ s= 4.599 GeV we made a first measurement of semileptonic Λc →Λeνe decays. In this article we briefly report these results.

Leptonic, semileptonic and rare charm decays at the BES-III experiment