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.
Acknowledgements
The author would like to thank Jing Zhao and Junxian Li for their comments on an early draft of this paper and Chris Hughes for some clarifying remarks. The author is also grateful to the referee for a thorough reading of the paper and their comments which helped improve it.
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- On the asymptotics of the shifted sums of Hecke eigenvalue squares
- On the splitting conjecture in the hybrid model for the Riemann zeta function
- Almost Dedekind domains without radical factorization
- Groups in which the centralizer of any non-central primary element is maximal
- GKM actions on cohomogeneity one manifolds
- Gruenberg–Kegel graphs: Cut groups, rational groups and the prime graph question
- Sobolev regularity for nonlinear Poisson equations with Neumann boundary conditions on Riemannian manifolds
- Higher differentiability for bounded solutions to a class of obstacle problems with (p,q)-growth
- Measures of noncompactness of interpolated polynomials
- The homotopy category of acyclic complexes of pure-projective modules
- The Gelfand–Kirillov dimension of Hecke–Kiselman algebras
- Sharp Li–Yau inequalities for Dunkl harmonic oscillators
- A Shimura–Shintani correspondence for rigid analytic cocycles of higher weight
- Free polynilpotent groups and the Magnus property
Articles in the same Issue
- Frontmatter
- On the asymptotics of the shifted sums of Hecke eigenvalue squares
- On the splitting conjecture in the hybrid model for the Riemann zeta function
- Almost Dedekind domains without radical factorization
- Groups in which the centralizer of any non-central primary element is maximal
- GKM actions on cohomogeneity one manifolds
- Gruenberg–Kegel graphs: Cut groups, rational groups and the prime graph question
- Sobolev regularity for nonlinear Poisson equations with Neumann boundary conditions on Riemannian manifolds
- Higher differentiability for bounded solutions to a class of obstacle problems with (p,q)-growth
- Measures of noncompactness of interpolated polynomials
- The homotopy category of acyclic complexes of pure-projective modules
- The Gelfand–Kirillov dimension of Hecke–Kiselman algebras
- Sharp Li–Yau inequalities for Dunkl harmonic oscillators
- A Shimura–Shintani correspondence for rigid analytic cocycles of higher weight
- Free polynilpotent groups and the Magnus property