Luminosity functions and overdensity of galaxies identified around the central QSO. Upper panel: cumulative R-band luminosity function of the MQN01 galaxies found within |Δv|≤1000 km s⁻¹ from the redshift of the QSO (black stars), compared to that of the “MUSE-FIELD” sample (black pentagons) and of the control sample of sources found in the MQN01 MUSE FoV within 2.5 < z < 4.5, masking |Δv|≤1500 km s⁻¹ around the QSO (orange diamonds). The vertical dotted line shows the magnitude at which the luminosity function of the spectroscopic samples flattens relative to the completeness-corrected one from Reddy & Steidel (2009). Lower panel: overdensity as a function of the R-band magnitude.