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Capítulo de Libro
On the sign of the real part of the Riemann zeta-function
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 | Lune, Jan van de | 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 |
dcterms.identifier | https://ror.org/03yxnpp24 | |
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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