A search is performed for new resonant high-mass phenomena in the dielectron final state. The search uses 36.1 $\mathrm{fb}^{-1}$ of proton-proton collision data, collected at $\sqrt{s} = 13$ TeV by the ATLAS experiment at the Large Hadron Collider during its 2015 and 2016 data-taking runs. The dielectron invariant mass is used as the search variable. No significant deviations from the Standard Model prediction are observed. Upper limits at the 95\% credibility level are set on the cross section times branching fraction to dielectron pairs for resonant $Z^{\prime}$ models considered in the search. Lower limits on the resonance pole mass are also presented. For the $Z^{\prime}_{\mathrm{SSM}}$, masses are excluded up to 4.5 TeV, while masses up to 4.1 TeV are excluded in the $E_{6}$-motivated $Z^{\prime}_{\chi}$ model. Limits are also derived in the Minimal $Z^{\prime}$ Model on the relative coupling strength $\gamma^{\prime}$. In addition, a series of studies are conducted in order to assess and reduce the dominant systematic uncertainty of this analysis, which arises from the imprecise knowledge of the Parton Distribution Functions in regions of very high parton $x$. While this uncertainty does not limit the discovery potential of the analysis presented here, it has the potential to do so in future searches. A novel approach is developed, and is shown to significantly reduce this systematic uncertainty in the high-mass search region of interest, thereby improving the discovery potential of future analyses.
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