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\(_a\)).

Metadaten
Author:	Jörn Steuding, Ade Irma Suriajaya
URN:	urn:nbn:de:bvb:20-opus-232621
Document Type:	Journal article
Faculties:	Fakultät für Mathematik und Informatik / Institut für Mathematik
Language:	English
Parent Title (English):	Computational Methods and Function Theory
ISSN:	1617-9447
Year of Completion:	2020
Volume:	20
Pagenumber:	389–401
Source:	Computational Methods and Function Theory 20, 389–401 (2020). https://doi.org/10.1007/s40315-020-00316-x
DOI:	https://doi.org/10.1007/s40315-020-00316-x
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):	CC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International