  Inclusive production of $D^*(2010)$ mesons in deep inelastic scattering has
been measured with the ZEUS detector at HERA using an integrated luminosity of
81.9 pb$^{-1}$. The decay channel $D^{* +}\to D^0 \pi^+ $ with $D^0\to
K^-\pi^+$ and corresponding antiparticle decay were used to identify $D^*$
mesons. Differential $D^*$ cross sections with $1.5<Q^2<1000$ GeV$^2$ and
$0.02<y<0.7$ in the kinematic region $1.5<p_T(D^*)<15$ GeV and
$|\eta(D^*)|<1.5$ are compared to different QCD calculations incorporating
different parameterisations of the parton densities in the proton. The data
show sensitivity to the gluon distribution in the proton and are reasonably
well described by next-to-leading-order QCD with the ZEUS NLO QCD fit used as
the input parton density in the proton. The observed cross section is
extrapolated to the full kinematic region in $p_T(D^*)$ and $\eta(D^*)$ in
order to determine the open-charm contribution, $F_2^{\rm charm}(x,Q^2)$, to
the proton structure function, $F_2$. Since, at low $Q^2$, the uncertainties of
the data are comparable to those from the QCD fit, the measured differential
cross sections in $y$ and $Q^2$ should be used in future fits to constrain the
gluon density.
