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Bounded Solutions of a Complex Differential Equation for the Riemann Hypothesis

30 June 2025, Version 21
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This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.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

We investigate the relationship between differential equations and the Riemann zeta function. We identify a more flexible function whose zeros coincide with the non-trivial zeros of the zeta function. We prove that every zero of this new function has a real part equal to $\frac{1}{2}$.

Keywords

Zeta function
Non trivial zeros
Riemann hypothesis

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Version History

Jun 30, 2025 Version 21

Version Notes

The numerical results are consistent with the findings of this manuscript.

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License

All Rights Reserved

DOI

10.33774/coe-2023-sb63n-v21
D O I: 10.33774/coe-2023-sb63n-v21 [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) declare that they have sought and gained approval from the relevant ethics committee/IRB for this research and its publication.

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