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dc.contributor.authorBroughan, Kevin A.
dc.contributor.authorBarnett, A. Ross
dc.date.accessioned2008-11-04T01:45:27Z
dc.date.available2008-11-04T01:45:27Z
dc.date.issued2003-11
dc.identifier.citationBroughan, K.A. & Barnett, A.R.(2003). The holomorphic flow of the Riemann zeta function . Mathematics of Computation, 73, 987-1004.en_US
dc.identifier.issn1088-6842
dc.identifier.urihttps://hdl.handle.net/10289/1263
dc.description.abstractThe flow of the Riemann zeta function, ś = ς(s), is considered, and phase portraits are presented. Attention is given to the characterization of the flow lines in the neighborhood of the first 500 zeros on the critical line. All of these zeros are foci. The majority are sources, but in a small proportion of exceptional cases the zero is a sink. To produce these portraits, the zeta function was evaluated numerically to 12 decimal places, in the region of interest, using the Chebyshev method and using Mathematica. The phase diagrams suggest new analytic properties of zeta, of which some are proved and others are given in the form of conjectures.en_US
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.publisherAmerican Mathematical Societyen_NZ
dc.rightsFirst published in Mathematics of Computation in volume 73, pages 987-1004, published by the American Mathematical Society. Copyright 2003, American Mathematical Society.en_US
dc.subjectDynamical systemen_US
dc.subjectphase portraiten_US
dc.subjectcritical pointen_US
dc.subjectorbiten_US
dc.subjectseparatrixen_US
dc.subjectRiemann zeta functionen_US
dc.titleThe holomorphic flow of the Riemann zeta functionen_US
dc.typeJournal Articleen_US
dc.identifier.doi10.1090/S0025-5718-03-01529-1en_US
dc.relation.isPartOfMathematics of Computationen_NZ
pubs.begin-page987en_NZ
pubs.editionMayen_NZ
pubs.elements-id28832
pubs.end-page1004en_NZ
pubs.issue246en_NZ
pubs.volume73en_NZ
uow.identifier.article-no246en_NZ


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