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

TL;DR

This paper proves the splitting conjecture in the hybrid model for the Riemann zeta function under the Riemann hypothesis, extending its validity to a larger parameter range and confirming the asymptotic splitting conjecture for specific moments.

Contribution

It extends the validity of the splitting conjecture in the hybrid model to a broader parameter range and verifies the asymptotic splitting conjecture for second and fourth moments.

Findings

Splitting conjecture holds to order under Riemann hypothesis.

Results valid for larger parameter X range.

Asymptotic splitting conjecture confirmed for second and fourth moments.

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.