Context : The faint-end slopes of galaxy luminosity functions ( LFs ) in clusters of galaxies have been observed in some cases to vary with clustercentric distance and should be influenced by physical processes ( mergers , tides ) affecting cluster galaxies .
However , there is a wide disagreement on the values of the faint-end LF slopes , ranging from -1 to -2.3 in the magnitude range -18 < M _ { r } < -14 .

Aims : We investigate the LF in the very relaxed cluster Abell 496 .

Methods : Our analysis is based on deep images obtained at CFHT with MegaPrime/MegaCam in four bands ( u ^ { * } g ^ { \prime } r ^ { \prime } i ^ { \prime } ) covering a 1 \times 1 deg ^ { 2 } region , which is centered on the cluster Abell 496 and extends to near its virial radius .
The LFs are estimated by statistically subtracting a reference field taken as the mean of the 4 Deep fields of the CFHTLS survey .
Background contamination is minimized by cutting out galaxies redder than the observed Red Sequence in the g ^ { \prime } - i ^ { \prime } versus i ^ { \prime } colour-magnitude diagram .

Results : In Abell 496 , the global LFs show a faint-end slope of -1.55 \pm 0.06 and vary little with observing band .
Without colour cuts , the LFs are much noisier but not significantly steeper .
The faint-end slopes show a statistically significant steepening from \alpha = -1.4 \pm 0.1 in the central region ( extending to half a virial radius ) to -1.8 \pm 0.1 in the Southern envelope of the cluster .
Cosmic variance and uncertain star-galaxy separation are our main limiting factors in measuring the faint-end of the LFs .
The large-scale environment of Abell 496 , probed with the fairly complete 6dFGS catalogue , shows a statistically significant 36 Mpc long filament at PA = 137 ^ { \circ } , but we do not find an enhanced LF along this axis .

Conclusions : Our LFs do not display the large number of dwarf galaxies ( \alpha \approx - 2 ) inferred by several authors , whose analyses may suffer from field contamination caused by inexistent or inadequate colour cuts .
Alternatively , different clusters may have different faint-end slopes , but this is hard to reconcile with the wide range of slopes found for given clusters and for wide sets of clusters .