  We present the results of a BeppoSAX observation of the fastest rotating
pulsar known: PSR B1937+21. The ~200 ks observation (78.5 ks MECS/34 ks LECS
on-source time) allowed us to investigate with high statistical significance
both the spectral properties and the pulse profile shape. The pulse profile is
clearly double peaked at energies > ~4 keV. Peak widths are compatible with the
instrumental time resolution and the second pulse lags the main pulse 0.52 in
phase, like is the case in the radio. In the 1.3-4 keV band we detect a ~45% DC
component; conversely the 4-10 keV pulsed fraction is consistent with 100%. The
on-pulse spectrum is fitted with an absorbed power-law of spectral index ~1.2,
harder than that of the total flux which is ~1.9. The total unabsorbed (2-10
keV) flux is F_{2-10} = 4.1 10^-13 cgs, implying a luminosity of L_X = 5.0
10^31 \Theta (d/3.6 kpc)^2 erg s^-1 and a X-ray efficiency of \eta = 4.5 10^-5
\Theta, where \Theta is the solid angle spanned by the emission beam. These
results are in agreement with those obtained by ASCA and a more recent
Rossi-XTE observation. The hydrogen column density N_H ~2 10^22 cm^-2 is ~10
times higher than expected from the radio dispersion measure and average
Galactic density of e-. Though it is compatible (within 2\sigma) with the
Galactic (HI derived) value of ~1 10^22 cm^-2, inspection of dust extinction
maps reveal that the pulsar falls in a highly absorbed region. In addition, 1.4
GHz radio map shows that the nearby (likely unrelated) HII source 4C21.53W is
part of a circular emission region ~4' across.
