Moments of CβE field partition function, Sineβ correlations and stochastic zeta
Abstract
We prove a conjecture of Fyodorov and Keating on the supercritical moments of the partition function of the CβE field or equivalently the supercritical moments of moments of the characteristic polynomial of the CβE ensemble for general β>0 and general real moment exponents. Moreover, we give the first expression for all correlation functions of the Sineβ point process for all β>0. The main object behind both results is the Hua-Pickrell stochastic zeta function introduced by Li and Valk\'o.
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