Direct searches for lepton flavor violation in decays of the Z boson with the ATLAS detector at the LHC are presented. Decays of the Z boson into an electron or muon and a hadronically decaying τ lepton are considered. The searches are based on a data sample of proton-proton collisions collected by the ATLAS detector in 2015 and 2016, corresponding to an integrated luminosity of 36.1 fb−1 at a center-of-mass energy of √s=13 TeV. No statistically significant excess of events above the expected background is observed, and upper limits on the branching ratios of lepton-flavor-violating decays are set at the 95% confidence level: B(Z→eτ)<5.8×10−5 and B(Z→μτ)<2.4×10−5. This is the first limit on B(Z→eτ) with ATLAS data. The upper limit on B(Z→μτ) is combined with a previous ATLAS result based on 20.3 fb−1 of proton-proton collision data at a center-of-mass energy of √s=8 TeV and the combined upper limit at 95% confidence level is B(Z→μτ)<1.3×10−5.1 MoreReceived 26 April 2018DOI:https://doi.org/10.1103/PhysRevD.98.092010Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.© 2018 CERN, for the ATLAS CollaborationPhysics Subject Headings (PhySH)Physical SystemsGauge bosonsW & Z bosonsPropertiesFlavor symmetriesTechniquesArtificial neural networksParticle data analysisParticles & Fields