The evolution of the UV luminosity and stellar mass functions of
  Lyman-alpha emitters from z~2 to z~6
  We measure the evolution of the rest-frame UV luminosity function (LF) and
the stellar mass function (SMF) of Lyman-alpha (Lya) emitters (LAEs) from z~2
to z~6 by exploring ~4000 LAEs from the SC4K sample. We find a correlation
between Lya luminosity (LLya) and rest-frame UV (M_UV), with best-fit
M_UV=-1.6+-0.2 log10(LLya/erg/s)+47+-12 and a shallower relation between LLya
and stellar mass (Mstar), with best-fit log10( Mstar/Msun)=0.9+-0.1
log10(LLya/erg/s)-28+-4.0. An increasing LLya cut predominantly lowers the
number density of faint M_UV and low Mstar LAEs. We estimate a proxy for the
full UV LFs and SMFs of LAEs with simple assumptions of the faint end slope.
For the UV LF, we find a brightening of the characteristic UV luminosity
(M_UV*) with increasing redshift and a decrease of the characteristic number
density (Phi*). For the SMF, we measure a characteristic stellar mass
(Mstar*/Msun) increase with increasing redshift, and a Phi* decline. However,
if we apply a uniform luminosity cut of log10 (LLya/erg/s) >= 43.0, we find
much milder to no evolution in the UV and SMF of LAEs. The UV luminosity
density (rho_UV) of the full sample of LAEs shows moderate evolution and the
stellar mass density (rho_M) decreases, with both being always lower than the
total rho_UV and rho_M of more typical galaxies but slowly approaching them
with increasing redshift. Overall, our results indicate that both rho_UV and
rho_M of LAEs slowly approach the measurements of continuum-selected galaxies
at z>6, which suggests a key role of LAEs in the epoch of reionisation.
