A search is presented for lepton-flavor violating decays of the Higgs boson to $\mu\tau$ and e$\tau$. The data set corresponds to an integrated luminosity of 137 fb$^{-1}$ collected at the LHC in proton-proton collisions at a center-of-mass energy of 13 TeV. No significant excess has been found, and the results are interpreted in terms of upper limits on lepton-flavor violating branching fractions of the Higgs boson. The observed (expected) upper limits on the branching fractions are, respectively, $\mathcal{B}($H $\to\mu\tau)$$\lt$ 0.15 (0.15)% and $\mathcal{B}($H$\to$e$\tau)$ $\lt$ 0.22 (0.16)% at 95% confidence level.
Measurements of the inclusive and differential fiducial cross sections of the Higgs boson are presented, using the $\tau$ lepton decay channel. The differential cross sections are measured as functions of the Higgs boson transverse momentum, jet multiplicity, and transverse momentum of the leading jet in the event if any. The analysis is performed using proton-proton data collected with the CMS detector at the LHC at a center-of-mass energy of 13 TeV and corresponding to an integrated luminosity of 138 fb$^{-1}$. These are the first differential measurements of the Higgs boson cross section in the final state of two $\tau$ leptons, and they constitute a significant improvement over measurements in other final states in events with a large jet multiplicity or with a Lorentz-boosted Higgs boson.