# The $a$-points of the Riemann zeta-function and the functional equation

Source: [The $a$-points of the Riemann zeta-function and the functional equation](<https://www.sota2.com/research/paper/68fa5c191e209131ce9ce21d>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T17:26:27.186Z

Authors: Athanasios Sourmelidis, J\\"orn Steuding, Ade Irma Suriajaya

Published: 2022-04-29T05:24:54.000Z

## Abstract

We prove an equivalent of the Riemann hypothesis in terms of the functional equation (in its asymmetrical form) and the $a$-points of the zeta-function, i.e., the roots of the equation $\\zeta(s)=a$, where $a$ is an arbitrary fixed complex number.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2204.13887>)

[PDF](<https://arxiv.org/pdf/2204.13887.pdf>)