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

Winston Heap

Type: Article

Publication Date: 2023-01-29

Citations: 3

DOI: https://doi.org/10.1515/forum-2022-0020

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.

Locations

arXiv (Cornell University) - View - PDF
Forum Mathematicum - View

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Works Cited by This (43)

Action	Title	Year	Authors
+	Sharp conditional bounds for moments of the Riemann zeta function	2013	Adam J. Harper
+ PDF Chat	A hybrid Euler–Hadamard product and moments of ζ'(ρ)	2013	Hung M. Bui S. M. Gonek Micah B. Milinovich
+	Fractional Moments of the Riemann Zeta-Function	1981	D. R. Heath‐Brown
+ PDF Chat	Moments of the Riemann zeta function	2009	K. Soundararajan
+	Hilbert's Inequality	1974	Hugh L. Montgomery R. C. Vaughan
+ PDF Chat	High moments of the Riemann zeta-function	2001	J. Brian Conrey S. M. Gonek
+ PDF Chat	On the mean values of Dirichlet <i>L</i> -functions	2007	Hung M. Bui Jonathan P. Keating
+ PDF Chat	On the mean values of <i>L</i> -functions in orthogonal and symplectic families	2007	Hung M. Bui Jonathan P. Keating
+	Mean-Value Theorems in the Theory of the Riemann Zeta-Function	1928	A. E. Ingham
+ PDF Chat	Contributions to the theory of the riemann zeta-function and the theory of the distribution of primes	1916	G. H. Hardy J. E. Littlewood