WINN, B., 2012. Derivative moments for characteristic polynomials from the CUE. Communications in Mathematical Physics, 315(2), pp.531-562.
We calculate joint moments of the characteristic polynomial of a random unitary
matrix from the circular unitary ensemble and its derivative in the case that the power
in themoments is an odd positive integer. The calculations are carried out for finite matrix
size and in the limit as the size of the matrices goes to infinity. The latter asymptotic
calculation allows us to prove a long-standing conjecture from random matrix theory.
The final publication is available at Springer via http://dx.doi.org/10.1007/s00220-012-1512-1