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

Abstract

We show that the splitting conjecture in the hybrid model of Gonek--Hughes--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.

47 pages