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dc.contributor.authorBroughan, Kevin A.
dc.date.accessioned2009-02-18T01:06:53Z
dc.date.available2009-02-18T01:06:53Z
dc.date.issued2005
dc.identifier.citationBroughan, K.A. (2005). The holomorphic flow of Riemann’s function ξ(z). Nonlinearity, 18(3), 1269-1294.en
dc.identifier.urihttps://hdl.handle.net/10289/2027
dc.description.abstractThe holomorphic flow z = ξ(z) of Riemann’s xi function is considered. Phase portraits are plotted and the following results, suggested by the portraits, proved: all separatrices tend to the positive and/or negative real axes. These are an infinite number of crossing separatrices. In the region between each pair of crossing separatrices- a band- there is at most one zero on the critical line. All zeros on the critical line are centres or have all elliptic sectors. The flows for ξ(z) and cosh (z) are linked with a differential equation. Simple zeros on the critical line and Gram points never coincide. The Riemann hypothesis is equivalent to all zeros being centres or multiple together with the non-existence of separatices which enter and leave a band in the same half plane.en
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.publisherInstitute of Physics Publishingen_NZ
dc.rightsThis article has been published in the journal: Nonlinearity. ©2005 IOP Publishing Ltd and London Mathematical Society.en
dc.subjectRiemann’s function Xi(s)en
dc.titleThe holomorphic flow of Riemann’s function ξ(z)en
dc.typeJournal Articleen
dc.identifier.doi10.1088/0951-7715/18/3/017en
dc.relation.isPartOfNonlinearityen_NZ
pubs.begin-page1269en_NZ
pubs.elements-id30732
pubs.end-page1294en_NZ
pubs.issue3en_NZ
pubs.volume18en_NZ


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