  A measurement using a one-electron quantum cyclotron gives the electron
magnetic moment in Bohr magnetons, g/2 = 1.001 159 652 180 73 (28) [0.28 ppt],
with an uncertainty 2.7 and 15 times smaller than for previous measurements in
2006 and 1987. The electron is used as a magnetometer to allow lineshape
statistics to accumulate, and its spontaneous emission rate determines the
correction for its interaction with a cylindrical trap cavity. The new
measurement and QED theory determine the fine structure constant, with
alpha^{-1} = 137.035 999 084 (51) [0.37 ppb], and an uncertainty 20 times
smaller than for any independent determination of alpha.
