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{\large\bf\boldmath  Measurement of $D^{\ast}$ Meson Cross Sections
at HERA and Determination of the Gluon Density in the Proton using NLO QCD
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{H1 Collaboration}\\                            
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{\small \em DESY, Hamburg, Germany}\\[6mm]
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With the H1 detector at the $ep$ collider HERA, 
$D^{\ast}$ meson production cross sections
have been measured 
in deep inelastic scattering 
with four-momentum transfers $Q^2>2$ GeV$^2$
and in photoproduction at energies around 
$W_{\gamma p}\approx 88$ GeV and $194$ GeV.
Next-to-Leading Order QCD calculations are found to describe
the differential cross sections within theoretical 
and experimental uncertainties. 
Using these calculations,
the NLO gluon momentum distribution in the proton, 
$x_g g(x_g)$, has been extracted 
in the momentum fraction range $7.5\cdot 10^{-4}< x_g <4\cdot 10^{-2}$
at average scales $\mu^2 =$ 25 to 50 GeV$^2$.
The gluon momentum fraction $x_g$ 
has been obtained
from the measured kinematics of the scattered electron and the 
$D^{\ast}$ meson in the final state.
The results compare well with the gluon distribution obtained from 
the analysis of scaling violations of the proton structure function $F_2$.

\vspace*{0.5cm}

{\bf References }\\
1. H1 Collaboration, C.~Adloff {\it et al}, 
DESY-98-204 / submitted to Nucl. Phys. B 
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