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The Riemann hypothesis is false

30 May 2022, Version 1
Working Paper
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

Let Theta be the supremum of the real parts of the zeros of the Riemann zeta function. We demonstrate in this note that Theta must be at least 3/4. This disproves the Riemann hypothesis, which asserts that Theta = 1/2.

Keywords

Riemann zeta function
Analytic number theory
zeros
Riemann hypothesis
false

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Version History

May 30, 2022 Version 1

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The content is available under CC BY 4.0 [opens in a new tab]

DOI

10.33774/coe-2022-vwztz
D O I: 10.33774/coe-2022-vwztz [opens in a new tab]

Author’s competing interest statement

The author(s) have declared they have no conflict of interest with regard to this content

Ethics

The author(s) have declared ethics committee/IRB approval is not relevant to this content

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