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On the sign of the real part of the Riemann zeta-function

 

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dc.contributor.editor Borwein, Jonathan M. es
dc.contributor.editor Shparlinski, Igor es
dc.contributor.editor Zudilin, Wadim es
dc.creator Arias de Reyna Martínez, Juan es
dc.creator Brent, Richard P. es
dc.creator Van de Lune, Jan es
dc.date.accessioned 2016-10-19T10:51:36Z
dc.date.available 2016-10-19T10:51:36Z
dc.date.issued 2013
dc.identifier.isbn 9781461466413 es
dc.identifier.isbn 9781461466420 es
dc.identifier.issn 2194-1009 es
dc.identifier.issn 2194-1017 es
dc.identifier.uri http://hdl.handle.net/11441/47773
dc.description.abstract We consider the distribution of argζ(σ +it) on fixed lines σ > 1/2, and in particular the density d(σ) = lim T→+∞ 1/2T |{t ∈ [−T,+T] : |argζ(σ +it)| > π/2}|, and the closely related density d−(σ) = lim T→+∞ 1/2T |{t ∈ [−T,+T] : ℜζ(σ +it) < 0}|. Using classical results of Bohr and Jessen, we obtain an explicit expression for the characteristic function ψσ(x) associated with argζ(σ + it). We give explicit expressions for d(σ) and d−(σ) in terms of ψσ(x). Finally, we give a practical algorithm for evaluating these expressions to obtain accurate numerical values of d(σ) and d−(σ). es
dc.format application/pdf es
dc.language.iso eng es
dc.publisher Springer es
dc.relation.ispartof Number Theory and Related Fields es
dc.rights Attribution-NonCommercial-NoDerivatives 4.0 Internacional *
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/ *
dc.title On the sign of the real part of the Riemann zeta-function es
dc.type info:eu-repo/semantics/bookPart es
dc.type.version info:eu-repo/semantics/submittedVersion es
dc.rights.accessrights info:eu-repo/semantics/openAccess es
dc.contributor.affiliation Universidad de Sevilla. Departamento de Análisis Matemático es
dc.relation.publisherversion http://download.springer.com/static/pdf/521/chp%253A10.1007%252F978-1-4614-6642-0_3.pdf?originUrl=http%3A%2F%2Flink.springer.com%2Fchapter%2F10.1007%2F978-1-4614-6642-0_3&token2=exp=1476875263~acl=%2Fstatic%2Fpdf%2F521%2Fchp%25253A10.1007%25252F978-1-4614-6642-0_3.pdf%3ForiginUrl%3Dhttp%253A%252F%252Flink.springer.com%252Fchapter%252F10.1007%252F978-1-4614-6642-0_3*~hmac=9d02098cd601902774d534f95e97ba06b6e7c2b833e9ce0e11cf53f52840b892 es
dc.identifier.doi 10.1007/978-1-4614-6642-0 3 es
dc.contributor.group Universidad de Sevilla. FQM104: Analisis Matematico es
idus.format.extent 22 p. es
dc.publication.initialPage 75 es
dc.publication.endPage 97 es
dc.relation.publicationplace New York es
dc.identifier.idus https://idus.us.es/xmlui/handle/11441/47773
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