## Abstract

Keating and Snaith modeled the Riemann zeta-function ζ(*s*) by characteristic polynomials of random *N*×*N* unitary matrices, and used this to conjecture the asymptotic main term for the 2*k*-th moment of ζ(1/2+*i**t*) when
*k* > -1/2. However, an arithmetical factor, widely believed to be part of the leading term coefficient, had to be inserted in an *ad hoc* manner. Gonek, Hughes and Keating later developed a hybrid formula for ζ(*s*) that combines a truncation of its Euler product with a product over its zeros. Using it, they recovered the moment conjecture of Keating and Snaith in a way that naturally includes the arithmetical factor. Here we use the hybrid formula to recover a conjecture of Hughes, Keating and O'Connell concerning the discrete moments of the derivative of the Riemann zeta-function averaged over the zeros of ζ(*s*), incorporating the arithmetical factor in a natural way.

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