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The production cross-sections for $W^{\pm}$ and $Z$ bosons are measured usingATLAS data corresponding to an integrated luminosity of 4.0 pb$^{-1}$ collectedat a centre-of-mass energy $\sqrt{s}=2.76$ TeV. The decay channels $W\rightarrow \ell \nu$ and $Z \rightarrow \ell \ell $ are used, where $\ell$ canbe an electron or a muon. The cross-sections are presented for a fiducialregion defined by the detector acceptance and are also extrapolated to the fullphase space for the total inclusive production cross-section. The combined(average) total inclusive cross-sections for the electron and muon channelsare:  \begin{eqnarray} \sigma^{\text{tot}}_{W^{+}\rightarrow \ell \nu}& = & 2312\pm 26\ (\text{stat.})\ \pm 27\ (\text{syst.}) \pm 72\ (\text{lumi.}) \pm 30\(\text{extr.})\text{pb} \nonumber, \\ \sigma^{\text{tot}}_{W^{-}\rightarrow\ell \nu}& = & 1399 \pm 21\ (\text{stat.})\ \pm 17\ (\text{syst.}) \pm 43\(\text{lumi.}) \pm 21\ (\text{extr.})\text{pb} \nonumber, \\\sigma^{\text{tot}}_{Z \rightarrow \ell \ell}& = & 323.4 \pm 9.8\(\text{stat.}) \pm 5.0\ (\text{syst.}) \pm 10.0\ (\text{lumi.}) \pm 5.5(\text{extr.}) \text{pb} \nonumber. \end{eqnarray} Measured ratios andasymmetries constructed using these cross-sections are also presented. Theseobservables benefit from full or partial cancellation of many systematicuncertainties that are correlated between the different measurements.

Measurement of $W^{\pm}$-boson and $Z$-boson production cross-sections in $pp$ collisions at $\sqrt{s}=2.76$ TeV with the ATLAS detector