# Value-Distribution of the Riemann Zeta-Function along its Julia Lines

Source: [Value-Distribution of the Riemann Zeta-Function along its Julia Lines](<https://www.sota2.com/research/paper/68fa587b1e209131ce9aeba8>)

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

Data updated: 2025-10-25T15:22:37.449Z

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

Published: 2020-07-29T08:15:27.000Z

## Abstract

For an arbitrary complex number $a\\neq 0$ we consider the distribution of values of the Riemann zeta-function $\\zeta$ at the $a$-points of the function $\\Delta$ which appears in the functional equation $\\zeta(s)=\\Delta(s)\\zeta(1-s)$. These $a$-points $\\delta\_a$ are clustered around the critical line $1/2+i\\mathbb{R}$ which happens to be a Julia line for the essential singularity of $\\zeta$ at infinity. We observe a remarkable average behaviour for the sequence of values $\\zeta(\\delta\_a)$.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2007.14661>)

[PDF](<https://arxiv.org/pdf/2007.14661.pdf>)