  We present measurements of the galaxy cluster X-ray Luminosity Function (XLF)
from the Wide Angle ROSAT Pointed Survey (WARPS) and quantify its evolution.
WARPS is a serendipitous survey of the central region of ROSAT pointed
observations and was carried out in two phases (WARPS-I and WARPS-II). The
results here are based on a final sample of 124 clusters, complete above a flux
limit of 6.5 10E-15 erg/s/cm2, with members out to redshift z ~ 1.05, and a sky
coverage of 70.9 deg2. We find significant evidence for negative evolution of
the XLF, which complements the majority of X-ray cluster surveys. To quantify
the suggested evolution, we perform a maximum likelihood analysis and conclude
that the evolution is driven by a decreasing number density of high luminosity
clusters with redshift, while the bulk of the cluster population remains nearly
unchanged out to redshift z ~ 1.1, as expected in a low density Universe. The
results are found to be insensitive to a variety of sources of systematic
uncertainty that affect the measurement of the XLF and determination of the
survey selection function. We perform a Bayesian analysis of the XLF to fully
account for uncertainties in the local XLF on the measured evolution, and find
that the detected evolution remains significant at the 95% level. We observe a
significant excess of clusters in the WARPS at 0.1 < z < 0.3 and LX ~ 2 10E42
erg/s compared with the reference low-redshift XLF, or our Bayesian fit to the
WARPS data. We find that the excess cannot be explained by sample variance, or
Eddington bias, and is unlikely to be due to problems with the survey selection
function.
