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

  • Winston Heap EMAIL logo
Veröffentlicht/Copyright: 30. Januar 2023

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.

MSC 2010: 11M06

Communicated by Valentin Blomer


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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Received: 2022-01-17
Revised: 2022-11-17
Published Online: 2023-01-30
Published in Print: 2023-03-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 8.11.2025 von https://www.degruyterbrill.com/document/doi/10.1515/forum-2022-0020/pdf
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