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We describe the search for Lyman-break galaxies (LBGs) near thesub-millimeter bright starburst galaxy HFLS3 at $z$$=$6.34 and a study on theenvironment of this massive galaxy during the end of reionization.We performedtwo independent selections of LBGs on images obtained with the \textit{GranTelescopio Canarias} (GTC) and the \textit{Hubble Space Telescope} (HST) bycombining non-detections in bands blueward of the Lyman-break and colorselection. A total of 10 objects fulfilling the LBG selection criteria at$z$$>$5.5 were selected over the 4.54 and 55.5 arcmin$^2$ covered by our HSTand GTC images, respectively. The photometric redshift, UV luminosity, and thestar-formation rate of these sources were estimated with models of theirspectral energy distribution. These $z$$\sim$6 candidates have physicalproperties and number densities in agreement with previous results. The UVluminosity function at $z$$\sim$6 and a Voronoi tessellation analysis of thisfield shows no strong evidence for an overdensity of relatively bright objects(m$_{F105W}$$<$25.9) associated with \textit{HFLS3}. However, the over-densityparameter deduced from this field and the surface density of objects can notexcluded definitively the LBG over-density hypothesis. Moreover we identifiedthree faint objects at less than three arcseconds from \textit{HFLS3} withcolor consistent with those expected for $z$$\sim$6 galaxies. Deeper data areneeded to confirm their redshifts and to study their association with\textit{HFLS3} and the galaxy merger that may be responsible for the massivestarburst.

Environment of the submillimeter-bright massive starburst HFLS3 at $z\sim$6.34