We use recently evaluated radiative and nonperturbative corrections to production of heavy quarks by a vector current to give very precise theoretical calculations of the high energy (t1/2>=V2GeV) imaginary part of the photon vacuum polarization function, ImII(t). This allows us to improve the corresponding contributionas to the muon (or any other lepton) g-2 anomaly and to the running QED constan ont the Z, AQUED(Mz). This decreases the erron in the evaluations by a factor betwen two and six for the high energy contribution and by some 50 per cent for the overall result. We find for the hadronic contibutions ah=7113.4+=102.5*10-11 and AAh: 289.42+=4.35*10-4.14.40 Gx.12.38Bx,12.38 Lg, 12.30G d
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