We present a newly measured X-ray temperature function of galaxy clusters using a complete flux-limited sample of 61 clusters .
The sample is constructed with the total survey area of 8.14 steradians and the flux limit of 1.99 \times 10 ^ { -11 } ergs s ^ { -1 } cm ^ { -2 } in the 0.1–2.4 keV band .
X-ray temperatures and fluxes of the sample clusters were accurately measured with ASCA and ROSAT data .
The derived temperature function covers an unprecedentedly wide temperature range of 1.4-11 keV .
By fitting these data with theoretically predicted temperature functions given by the Press-Schechter formalism together with a recent formation approximation and the CDM power spectrum , we obtained tight and individual constraints on \Omega _ { m, 0 } and \sigma _ { 8 } .
We also employed the Formation-Epoch model in which the distribution in the formation epoch of clusters as well as the temperature evolution are taken into account , showing significantly different results .
Systematics caused by the uncertainty in the mass-temperature relation are studied and found to be as large as the statistical errors .