We present the results of a deep (J = 19.1?mag) infrared (ZY?JHK) survey over the full a Per open cluster extracted from the Data Release 9 of the United Kingdom Infrared Telescope Infrared Deep Sky Survey Galactic Clusters Survey (UKIDSS). We have selected similar to 700 cluster member candidates in similar to 56 square degrees in a Per by combining photometry in five near-infrared passbands and proper motions derived from the multiple epochs provided by the UKIDSS Galactic Clusters Survey (GCS) Data Release 9 (DR9). We also provide revised membership for all previously published a Per low-mass stars and brown dwarfs recovered in GCS based on the new photometry and astrometry provided by DR9. We find no evidence of K-band variability in members of a Per with dispersion less than 0.060.09?mag. We employed two independent but complementary methods to derive the cluster luminosity and mass functions: a probabilistic analysis and a more standard approach consisting of stricter astrometric and photometric cuts. We find that the resulting luminosity and mass functions obtained from both methods are consistent. We find that the shape of the a Per mass function is similar to that of the Pleiades although the characteristic mass may be higher after including higher mass data from earlier studies (the dispersion is comparable). We conclude that the mass functions of a Per, the Pleiades and Praesepe are best reproduced by a log-normal representation similar to the system field mass function although with some variation in the characteristic mass and dispersion values.