Products and Ratios of Characteristic Polynomials of Random Hermitian Matrices
نویسنده
چکیده
denotes the average of f with respect to dPa ,N . Recently there has been considerable interest in the averages of products and ratios of the characteristic polynomials DN@m ,H#5P i51 N (m2xi(H)) of random matrices with respect to various ensembles. Such averages are used, in particular, in making predictions about the moments of the Riemann-zeta function @see Refs. 12–14 ~circular ensembles! and 3 ~unitary ensembles!#. Many other uses are described, for example, in Refs. 1, 12, and 17. By ~1.2!, for unitary ensembles, such averages have the form
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