  The autocorrelation function of spectral determinants is proposed as a
convenient tool for the characterization of spectral statistics in general, and
for the study of the intimate link between quantum chaos and random matrix
theory, in particular. For this purpose, the correlation functions of spectral
determinants are evaluated for various random matrix ensembles, and are
compared with the corresponding semiclassical expressions. The method is
demonstrated by applying it to the spectra of the quantized Sinai billiards in
two and three dimensions.
