This paper describes precision measurements of the transverse momentum $$p_\mathrm {T}^{\ell \ell }$$
p
T
ℓ
ℓ
($$\ell =e,\mu $$
ℓ
=
e
,
μ
) and of the angular variable $$\phi ^{*}_{\eta }$$
ϕ
η
∗
distributions of Drell–Yan lepton pairs in a mass range of 66–116 GeV. The analysis uses data from 36.1 fb$$^{-1}$$
-
1
of proton–proton collisions at a centre-of-mass energy of $$\sqrt{s}=13\,$$
s
=
13
TeV collected by the ATLAS experiment at the LHC in 2015 and 2016. Measurements in electron-pair and muon-pair final states are performed in the same fiducial volumes, corrected for detector effects, and combined. Compared to previous measurements in proton–proton collisions at $$\sqrt{s}=7$$
s
=
7
and $$8\,$$
8
TeV, these new measurements probe perturbative QCD at a higher centre-of-mass energy with a different composition of initial states. They reach a precision of 0.2$$\%$$
%
for the normalized spectra at low values of $$p_\mathrm {T}^{\ell \ell }$$
p
T
ℓ
ℓ
. The data are compared with different QCD predictions, where it is found that predictions based on resummation approaches can describe the full spectrum within uncertainties.
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