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

Please always quote using this URN: urn:nbn:de:bvb:20-opus-232621
  • 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+i\(\mathbb {R}\) 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\(_a\)).

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Author: Jörn Steuding, Ade Irma Suriajaya
Document Type:Journal article
Faculties:Fakultät für Mathematik und Informatik / Institut für Mathematik
Parent Title (English):Computational Methods and Function Theory
Year of Completion:2020
Source:Computational Methods and Function Theory 20, 389–401 (2020).
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Tag:Julia line; Riemann zeta-function; critical line; value-distribution
MSC-Classification:11-XX NUMBER THEORY / 11Mxx Zeta and L-functions: analytic theory / 11M06 ζ(s) and L(s, χ)
30-XX FUNCTIONS OF A COMPLEX VARIABLE (For analysis on manifolds, see 58-XX) / 30Dxx Entire and meromorphic functions, and related topics / 30D35 Distribution of values, Nevanlinna theory
Release Date:2021/06/30
Licence (German):License LogoCC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International