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On the exact location of the non-trivial zeros of Riemann’s zeta function


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dc.creator Arias de Reyna Martínez, Juan es
dc.creator Van de Lune, Jan es 2016-07-01T07:46:59Z 2016-07-01T07:46:59Z 2014
dc.identifier.citation Arias de Reyna Martínez, J. y Van de Lune, J. (2014). On the exact location of the non-trivial zeros of Riemann’s zeta function. Acta Arithmetica, 163 (3), 215-245.
dc.identifier.issn 0065-1036 es
dc.identifier.issn 1730-6264 es
dc.description.abstract In this paper we introduce the real valued real analytic function κ(t) implicitly defined by e 2πiκ(t) = −e −2iϑ(t) ζ 0 ( 1 2 − it) ζ 0( 1 2 + it) , (κ(0) = − 1 2 ). By studying the equation κ(t) = n (without making any unproved hypotheses), we will show that (and how) this function is closely related to the (exact) position of the zeros of Riemann’s ζ(s) and ζ 0 (s). Assuming the Riemann hypothesis and the simplicity of the zeros of ζ(s), it will follow that the ordinate of the zero 1/2 + iγn of ζ(s) will be the unique solution to the equation κ(t) = n. es
dc.description.sponsorship Ministerio de Economía y Competitividad es
dc.format application/pdf es
dc.language.iso eng es
dc.publisher Polish Academy of Sciences, Institute of Mathematics es
dc.relation.ispartof Acta Arithmetica, 163 (3), 215-245.
dc.rights Attribution-NonCommercial-NoDerivatives 4.0 Internacional *
dc.rights.uri *
dc.subject Zeta function es
dc.subject Non-trivial zeros es
dc.subject Distribution of zeros es
dc.title On the exact location of the non-trivial zeros of Riemann’s zeta function es
dc.type info:eu-repo/semantics/article es
dc.type.version info:eu-repo/semantics/publishedVersion es
dc.rights.accessrights info:eu-repo/semantics/openAccess es
dc.contributor.affiliation Universidad de Sevilla. Departamento de Análisis Matemático es
dc.relation.projectID info:eu-repo/grantAgreement/MINECO/MTM2012-30748 es
dc.relation.publisherversion ES
dc.identifier.doi 10.4064/aa163-3-3 es Universidad de Sevilla. FQM104: Analisis Matematico es
idus.format.extent 28 p. es
dc.journaltitle Acta Arithmetica es
dc.publication.volumen 163 es
dc.publication.issue 3 es
dc.publication.initialPage 215 es
dc.publication.endPage 245 es
dc.contributor.funder Ministerio de Economía y Competitividad (MINECO). España
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