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A search is conducted for new resonant and non-resonant high-mass phenomena in dielectron and dimuon final states. The search uses 36.1 fb −1 of proton-proton collision data, collected at √ s = 13 TeV by the ATLAS experiment at the LHC in 2015 and 2016. No significant deviation from the Standard Model prediction is observed. Upper limits at 95% credibility level are set on the cross-section times branching ratio for resonances decaying into dileptons, which are converted to lower limits on the resonance mass, up to 4.1 TeV for the E 6 -motivated Z χ . Lower limits on the qq contact interaction scale are set between 2.4 TeV and 40 TeV, depending on the model. Conclusion 21A Dilepton invariant mass tables 22The ATLAS collaboration 44 IntroductionThis article presents a search for resonant and non-resonant new phenomena, based on the analysis of dilepton final states (ee and µµ) in proton-proton (pp) collisions with the ATLAS detector at the Large Hadron Collider (LHC) operating at √ s = 13 TeV. The data set was collected during 2015 and 2016, and corresponds to an integrated luminosity of 36.1 fb −1 . In the search for new physics carried out at hadron colliders, the study of -1 - JHEP10(2017)182dilepton final states provides excellent sensitivity to a large variety of phenomena. This experimental signature benefits from a fully reconstructed final state, high signal-selection efficiencies and relatively small, well-understood backgrounds, representing a powerful test for a wide range of theories beyond the Standard Model (SM).Models with extended gauge groups often feature additional U(1) symmetries with corresponding heavy spin-1 bosons. These bosons, generally referred to as Z , would manifest as a narrow resonance through its decay, in the dilepton mass spectrum. Among these models are those inspired by Grand Unified Theories, which are motivated by gauge unification or a restoration of the left-right symmetry violated by the weak interaction. Examples considered in this article include the Z bosons of the E 6 -motivated [1,2] theories as well as Minimal models [3]. The Sequential Standard Model (SSM) [2] is also considered due to its inherent simplicity and usefulness as a benchmark model. The SSM manifests a Z SSM boson with couplings to fermions equal to those of the SM Z boson.The most sensitive previous searches for a Z boson decaying into the dilepton final state were carried out by the ATLAS and CMS collaborations [4,5]. Using 3.2 fb −1 of pp collision data at √ s = 13 TeV collected in 2015, ATLAS set a lower exclusion limit at 95% credibility level (CL) on the Z SSM pole mass of 3.4 TeV for the combined ee and µµ channels. Similar limits were set by CMS using the 2015 data sample.This search is also sensitive to a series of other models that predict the presence of narrow dilepton resonances. These models include the Randall-Sundrum (RS) model [6] with a warped extra dimension giving rise to spin-2 graviton excitations, the quantum black-hole model [7], the Z * model [8], and the minimal wal...