Value-Distribution of the Riemann Zeta-Function Along Its Julia Lines

Jörn Steuding; Ade Irma Suriajaya

doi:10.1007/s40315-020-00316-x

Value-Distribution of the Riemann Zeta-Function Along Its Julia Lines

Jörn Steuding, Ade Irma Suriajaya

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

For an arbitrary complex number a≠ 0 we consider the distribution of values of the Riemann zeta-function ζ at the a-points of the function Δ which appears in the functional equation ζ(s) = Δ (s) ζ(1 - s). These a-points δ_a are clustered around the critical line 1 / 2 + iR which happens to be a Julia line for the essential singularity of ζ at infinity. We observe a remarkable average behaviour for the sequence of values ζ(δ_a).

Original language	English
Pages (from-to)	389-401
Number of pages	13
Journal	Computational Methods and Function Theory
Volume	20
Issue number	3-4
DOIs	https://doi.org/10.1007/s40315-020-00316-x
Publication status	Published - Nov 2020

All Science Journal Classification (ASJC) codes

Analysis
Computational Theory and Mathematics
Applied Mathematics

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AB - For an arbitrary complex number a≠ 0 we consider the distribution of values of the Riemann zeta-function ζ at the a-points of the function Δ which appears in the functional equation ζ(s) = Δ (s) ζ(1 - s). These a-points δa are clustered around the critical line 1 / 2 + iR which happens to be a Julia line for the essential singularity of ζ at infinity. We observe a remarkable average behaviour for the sequence of values ζ(δa).

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Value-Distribution of the Riemann Zeta-Function Along Its Julia Lines

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