We have detected pulsed X-ray emission from the fastest millisecond pulsar known, PSR B1937+21 (P=1.558 msec), with ASCA. The pulsar is detected as a point source above $sim 1.7$ keV, with no indication of nebulosity. The source flux in the 2--10 keV band is found to be $f = (3.7pm 0.6) times 10^{-13}$ erg s$^{-1}$ cm$^{-2}$, which implies an isotropic luminosity of $L_{rm x} = 4 pi D^2 f sim (5.7pm 1.0) times 10^{32} ~(D/3.6 {rm kpc})^2$ erg s$^{-1}$, where D is the distance, and an X-ray efficiency of $sim 5 times 10^{-4}$ relative to the spin-down power of the pulsar. The pulsation is found at the period predicted by the radio ephemeris with a very narrow primary peak, the width of which is about 1/16 phase ($sim 100 mu$s), near the time resolution limit ($61 mu$s) of the observation. The instantaneous flux in the primary peak (1/16 phase interval) is found to be ($4.0pm 0.8) times 10^{-12}$ erg s$^{-1}$ cm$^{-2}$. Although there is an indication for the secondary peak, we consider its statistical significance too low to claim a definite detection. The narrow pulse profile and the detection in the 2--10 keV band imply that the X-ray emission is caused by the magnetospheric particle acceleration. Comparison of X-ray and radio arrival times of pulses indicates, within the timing errors, that the X-ray pulse is coincident with the radio interpulse.
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