On the splitting conjecture in the hybrid model for the Riemann zeta function

Abstract

Abstract We show that the splitting conjecture in the hybrid model of Gonek, Hughes and Keating holds to order on the Riemann hypothesis. Our results are valid in a larger range of the parameter X which mediates between the partial Euler and Hadamard products. We also show that the asymptotic splitting conjecture holds for this larger range of X in the cases of the second and fourth moments.