  Differential Higgs boson (H) production cross sections are sensitive probes
for physics beyond the standard model. New physics may contribute in the
gluon-gluon fusion loop, the dominant Higgs boson production mechanism at the
LHC, and manifest itself through deviations from the distributions predicted by
the standard model. Combined spectra for the H $\to$ $\gamma\gamma$, H $\to$
ZZ, and H $\to$ $\mathrm{b\overline{b}}$ decay channels and the inclusive Higgs
boson production cross section are presented, based on proton-proton collision
data recorded with the CMS detector at $\sqrt{s} =$ 13 TeV corresponding to an
integrated luminosity of 35.9 fb$^{-1}$. The transverse momentum spectrum is
used to place limits on the Higgs boson couplings to the top, bottom, and charm
quarks, as well as its direct coupling to the gluon field. No significant
deviations from the standard model are observed in any differential
distribution. The measured total cross section is 61.1 $\pm$ 6.0 (stat) $\pm$
3.7 (syst) pb, and the precision of the measurement of the differential cross
section of the Higgs boson transverse momentum is improved by about 15% with
respect to the H $\to$ $\gamma\gamma$ channel alone.
