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A remark on density theorems for Riemann’s zeta-function

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Abstract

The goal of this paper is to give a relatively simple proof of some known zero density estimates for Riemann’s zeta-function which are sufficiently strong to break the density hypothesis for Re s > 7/8. Apart from a simple but ingenious idea of Halász the proof uses only classical knowledge about the zeta-function, results known for at least hundred years.

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Acknowledgements

This work was supported by the National Research Development and Innovation Office of Hungary, NKFIH, KKP 133819.

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Authors and Affiliations

  1. ELKH Alfréd Rényi Mathematical Institute, Budapest, H-1053, Hungary

    János Pintz

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  1. János Pintz
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Correspondence to János Pintz.

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Dedicated to the memory of Jing-run Chen on the occasion of the 50th anniversary of the publication of his celebrated (1 + 2) theorem on Goldbach’s conjecture

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Pintz, J. A remark on density theorems for Riemann’s zeta-function. Sci. China Math. 66, 2795–2802 (2023). https://doi.org/10.1007/s11425-023-2215-7

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