Moments of characteristic polynomials for classical β ensembles

Abstract

For random matrix ensembles with unitary symmetry, there is interest in the large N form of the moments of the absolute value of the characteristic polynomial for their relevance to the Riemann zeta function on the critical line, and to Fisher–Hartwig asymptotics in the theory of Toeplitz determinants. The constant (with respect to N) in this asymptotic expansion, involving the Barnes G function, is most relevant to the first of these, while the algebraic term (in N) and the functional dependence on the power are of primary interest in the latter. Desrosiers and Liu [Constr. Approx. 39, 273 (2014)] have obtained the analogous expansions for the classical Gaussian, Laguerre and Jacobi β ensem..