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We present the first estimate of the Ly{\alpha} luminosity function usingblind spectroscopy from the Multi Unit Spectroscopic Explorer, MUSE, in theHubble Deep Field South. Using automatic source-detection software, we assemblea homogeneously-detected sample of 59 Ly{\alpha} emitters covering a flux rangeof -18.0 < log10 (F) < -16.3 (erg s^-1 cm^-2), corresponding to luminosities of41.4 < log10 (L) < 42.8 (erg s^-1). As recent studies have shown, Ly{\alpha}fluxes can be underestimated by a factor of two or more via traditionalmethods, and so we undertake a careful assessment of each object's Ly{\alpha}flux using a curve-of-growth analysis to account for extended emission. Wedescribe our self-consistent method for determining the completeness of thesample, and present an estimate of the global Ly{\alpha} luminosity functionbetween redshifts 2.91 < z < 6.64 using the 1/Vmax estimator. We find theluminosity function is higher than many number densities reported in theliterature by a factor of 2 - 3, although our result is consistent at the1{\sigma} level with most of these studies. Our observed luminosity function isalso in good agreement with predictions from semi-analytic models, and shows noevidence for strong evolution between the high- and low-redshift halves of thedata. We demonstrate that one's approach to Ly{\alpha} flux estimation doesalter the observed luminosity function, and caution that accurate fluxassessments will be crucial in measurements of the faint end slope. This is apilot study for the Ly{\alpha} luminosity function in the MUSE deep-fields, tobe built on with data from the Hubble Ultra Deep Field which will increase thesize of our sample by almost a factor of 10.

MUSE Deep-Fields: The Lya Luminosity Function in the Hubble Deep Field South at 2.91 < z < 6.64