  A search is presented for new high-mass resonances decaying into electron or
muon pairs. The search uses proton-proton collision data at a centre-of-mass
energy of 13 TeV collected by the CMS experiment at the LHC in 2016,
corresponding to an integrated luminosity of 36 fb$^{-1}$. Observations are in
agreement with standard model expectations. Upper limits on the product of a
new resonance production cross section and branching fraction to dileptons are
calculated in a model-independent manner. This permits the interpretation of
the limits in models predicting a narrow dielectron or dimuon resonance. A scan
of different intrinsic width hypotheses is performed. Limits are set on the
masses of various hypothetical particles. For the Z$'_\mathrm{SSM}$
(Z$'_{\psi}$) particle, which arises in the sequential standard model
(superstring-inspired model), a lower mass limit of 4.50 (3.90) TeV is set at
95% confidence level. The lightest Kaluza-Klein graviton arising in the
Randall-Sundrum model of extra dimensions, with coupling parameters
$k/\overline{M}_\mathrm{Pl}$ of 0.01, 0.05, and 0.10, is excluded at 95%
confidence level below 2.10, 3.65, and 4.25 TeV, respectively. In a simplified
model of dark matter production via a vector or axial vector mediator, limits
at 95% confidence level are obtained on the masses of the dark matter particle
and its mediator.
