In:
Chaos: An Interdisciplinary Journal of Nonlinear Science, AIP Publishing, Vol. 20, No. 3 ( 2010-09-01)
Abstract:
When nonzero, the ζ function is intimately connected with numerical information processing. Two other functions play a key role, namely, η(s)=∑n≥1(−1)n+1/ns and λ(s)=∑n≥01/(2n+1)s. The paper opens on a survey of some of the seminal work of Euler [Mémoires Acad. Sci., Berlin 1768, 83 (1749)] and of the amazing theorem by Voronin [Math. USSR, Izv. 9, 443 (1975)] Then, as a follow-up of Chatelin [Qualitative Computing. A Computational Journey into Nonlinearity (World Scientific, Singapore, in press)], we present a fresh look at the triple (η,ζ,λ) which suggests an elementary analysis based on the distances of the three complex numbers z, z/2, and 2/z to 0 and 1. This metric approach is used to contextualize any nonlinear computation when it is observed at a point describing a complex plane. The results applied to ζ, η, and λ shed a new epistemological light about the critical line. The suggested interpretation related to ζ carries computational significance.
Type of Medium:
Online Resource
ISSN:
1054-1500
,
1089-7682
Language:
English
Publisher:
AIP Publishing
Publication Date:
2010
detail.hit.zdb_id:
1472677-4
SSG:
11
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