We calculate the charmonium correlators on the lattice with $n_f = 2+ 1$ Moebius domain wall fermion, and extract the charm quark mass and the strong coupling constant. Time moments are defined by current-current correlators, which have been calculated in the continuum theory by perturbation theory. We extract the charm quark mass by matching the lattice results with the corresponding perturbative QCD calculations, using the recently generated ensembles by the JLQCD collaboration at lattice spacings $a = 0.083, 0.055$, and $0.044$ fm.
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