Correlation of characteristic polynomials in random matrix ensembles                            
                              Friedrich Goetze
                        Department of Mathematics
                     University of Bielefeld, Germany

The local spectral distribution of eigenvalues of  Wigner
random matrices in the bulk of the spectrum is conjectured to be
universal after suitable scaling with a distribution determined by Gaussian
Wigner matrices. Here we discuss results concerning  the correlation coefficient of
chacteristic polynomials of Wigner matrices which yields in the limit
the correlation kernel  of the spectrum of Gaussian matrices. Analoguous
results for other ensembles of random   matrices and for correlations of
zeta-functions are discussed. This is joint work with H. Koesters.