A note on the zeros of approximations of the Ramanujan Ξ -function
Descripción del Articulo
In this paper we review the study of the distribution of the zeros of certain approximations for the Ramanujan Ξ -function given by Ki (Ramanujan J 17(1):123–143, 2008), and we provide new proofs of his results. Our approach is motivated by the ideas of Velásquez (J Anal Math 110:67–127, 2010) in th...
| Autores: | , |
|---|---|
| Formato: | artículo |
| Fecha de Publicación: | 2020 |
| Institución: | Consejo Nacional de Ciencia Tecnología e Innovación |
| Repositorio: | CONCYTEC-Institucional |
| Lenguaje: | inglés |
| OAI Identifier: | oai:repositorio.concytec.gob.pe:20.500.12390/2592 |
| Enlace del recurso: | https://hdl.handle.net/20.500.12390/2592 https://doi.org/10.1007/s11139-020-00321-7 |
| Nivel de acceso: | acceso abierto |
| Materia: | Zeros of approximations of the Ramanujan Ξ -function Distribution of zeros of entire functions Ramanujan zeta function Riemann hypothesis http://purl.org/pe-repo/ocde/ford#1.01.01 |
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Publicationrp06671600rp06672600Chirre A.Castañón O.V.2024-05-30T23:13:38Z2024-05-30T23:13:38Z2020https://hdl.handle.net/20.500.12390/2592https://doi.org/10.1007/s11139-020-00321-72-s2.0-85089996026In this paper we review the study of the distribution of the zeros of certain approximations for the Ramanujan Ξ -function given by Ki (Ramanujan J 17(1):123–143, 2008), and we provide new proofs of his results. Our approach is motivated by the ideas of Velásquez (J Anal Math 110:67–127, 2010) in the study of the zeros of certain sums of entire functions with some condition of stability related to the Hermite–Biehler theorem. © 2020, The Author(s).Fondo Nacional de Desarrollo Científico y Tecnológico - FondecytengSpringerRamanujan Journalinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/4.0/Zeros of approximations of the Ramanujan Ξ -functionDistribution of zeros of entire functions-1Ramanujan zeta function-1Riemann hypothesis-1http://purl.org/pe-repo/ocde/ford#1.01.01-1A note on the zeros of approximations of the Ramanujan Ξ -functioninfo:eu-repo/semantics/articlereponame:CONCYTEC-Institucionalinstname:Consejo Nacional de Ciencia Tecnología e Innovacióninstacron:CONCYTEC#PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE#20.500.12390/2592oai:repositorio.concytec.gob.pe:20.500.12390/25922024-05-30 15:25:05.679https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_14cbinfo:eu-repo/semantics/closedAccessmetadata only accesshttps://repositorio.concytec.gob.peRepositorio Institucional CONCYTECrepositorio@concytec.gob.pe#PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE#<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="18c188f8-80f2-4371-9340-f3ef47c2b5ab"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>A note on the zeros of approximations of the Ramanujan Ξ -function</Title> <PublishedIn> <Publication> <Title>Ramanujan Journal</Title> </Publication> </PublishedIn> <PublicationDate>2020</PublicationDate> <DOI>https://doi.org/10.1007/s11139-020-00321-7</DOI> <SCP-Number>2-s2.0-85089996026</SCP-Number> <Authors> <Author> <DisplayName>Chirre A.</DisplayName> <Person id="rp06671" /> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> <Author> <DisplayName>Castañón O.V.</DisplayName> <Person id="rp06672" /> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Springer</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>https://creativecommons.org/licenses/by/4.0/</License> <Keyword>Zeros of approximations of the Ramanujan Ξ -function</Keyword> <Keyword>Distribution of zeros of entire functions</Keyword> <Keyword>Ramanujan zeta function</Keyword> <Keyword>Riemann hypothesis</Keyword> <Abstract>In this paper we review the study of the distribution of the zeros of certain approximations for the Ramanujan Ξ -function given by Ki (Ramanujan J 17(1):123–143, 2008), and we provide new proofs of his results. Our approach is motivated by the ideas of Velásquez (J Anal Math 110:67–127, 2010) in the study of the zeros of certain sums of entire functions with some condition of stability related to the Hermite–Biehler theorem. © 2020, The Author(s).</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication> -1 |
| dc.title.none.fl_str_mv |
A note on the zeros of approximations of the Ramanujan Ξ -function |
| title |
A note on the zeros of approximations of the Ramanujan Ξ -function |
| spellingShingle |
A note on the zeros of approximations of the Ramanujan Ξ -function Chirre A. Zeros of approximations of the Ramanujan Ξ -function Distribution of zeros of entire functions Ramanujan zeta function Riemann hypothesis http://purl.org/pe-repo/ocde/ford#1.01.01 |
| title_short |
A note on the zeros of approximations of the Ramanujan Ξ -function |
| title_full |
A note on the zeros of approximations of the Ramanujan Ξ -function |
| title_fullStr |
A note on the zeros of approximations of the Ramanujan Ξ -function |
| title_full_unstemmed |
A note on the zeros of approximations of the Ramanujan Ξ -function |
| title_sort |
A note on the zeros of approximations of the Ramanujan Ξ -function |
| author |
Chirre A. |
| author_facet |
Chirre A. Castañón O.V. |
| author_role |
author |
| author2 |
Castañón O.V. |
| author2_role |
author |
| dc.contributor.author.fl_str_mv |
Chirre A. Castañón O.V. |
| dc.subject.none.fl_str_mv |
Zeros of approximations of the Ramanujan Ξ -function |
| topic |
Zeros of approximations of the Ramanujan Ξ -function Distribution of zeros of entire functions Ramanujan zeta function Riemann hypothesis http://purl.org/pe-repo/ocde/ford#1.01.01 |
| dc.subject.es_PE.fl_str_mv |
Distribution of zeros of entire functions Ramanujan zeta function Riemann hypothesis |
| dc.subject.ocde.none.fl_str_mv |
http://purl.org/pe-repo/ocde/ford#1.01.01 |
| description |
In this paper we review the study of the distribution of the zeros of certain approximations for the Ramanujan Ξ -function given by Ki (Ramanujan J 17(1):123–143, 2008), and we provide new proofs of his results. Our approach is motivated by the ideas of Velásquez (J Anal Math 110:67–127, 2010) in the study of the zeros of certain sums of entire functions with some condition of stability related to the Hermite–Biehler theorem. © 2020, The Author(s). |
| publishDate |
2020 |
| dc.date.accessioned.none.fl_str_mv |
2024-05-30T23:13:38Z |
| dc.date.available.none.fl_str_mv |
2024-05-30T23:13:38Z |
| dc.date.issued.fl_str_mv |
2020 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article |
| format |
article |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/20.500.12390/2592 |
| dc.identifier.doi.none.fl_str_mv |
https://doi.org/10.1007/s11139-020-00321-7 |
| dc.identifier.scopus.none.fl_str_mv |
2-s2.0-85089996026 |
| url |
https://hdl.handle.net/20.500.12390/2592 https://doi.org/10.1007/s11139-020-00321-7 |
| identifier_str_mv |
2-s2.0-85089996026 |
| dc.language.iso.none.fl_str_mv |
eng |
| language |
eng |
| dc.relation.ispartof.none.fl_str_mv |
Ramanujan Journal |
| dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess |
| dc.rights.uri.none.fl_str_mv |
https://creativecommons.org/licenses/by/4.0/ |
| eu_rights_str_mv |
openAccess |
| rights_invalid_str_mv |
https://creativecommons.org/licenses/by/4.0/ |
| dc.publisher.none.fl_str_mv |
Springer |
| publisher.none.fl_str_mv |
Springer |
| dc.source.none.fl_str_mv |
reponame:CONCYTEC-Institucional instname:Consejo Nacional de Ciencia Tecnología e Innovación instacron:CONCYTEC |
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Consejo Nacional de Ciencia Tecnología e Innovación |
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CONCYTEC |
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CONCYTEC |
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CONCYTEC-Institucional |
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CONCYTEC-Institucional |
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Repositorio Institucional CONCYTEC |
| repository.mail.fl_str_mv |
repositorio@concytec.gob.pe |
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1844883058538315776 |
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13.088272 |
Nota importante:
La información contenida en este registro es de entera responsabilidad de la institución que gestiona el repositorio institucional donde esta contenido este documento o set de datos. El CONCYTEC no se hace responsable por los contenidos (publicaciones y/o datos) accesibles a través del Repositorio Nacional Digital de Ciencia, Tecnología e Innovación de Acceso Abierto (ALICIA).
La información contenida en este registro es de entera responsabilidad de la institución que gestiona el repositorio institucional donde esta contenido este documento o set de datos. El CONCYTEC no se hace responsable por los contenidos (publicaciones y/o datos) accesibles a través del Repositorio Nacional Digital de Ciencia, Tecnología e Innovación de Acceso Abierto (ALICIA).
