Higher order turán inequalities for the Riemann ξ-function
dc.contributor.author | Dimitrov, Dimitar Kolev [UNESP] | |
dc.contributor.author | Lucas, Fábio R. | |
dc.contributor.institution | Universidade Estadual Paulista (Unesp) | |
dc.contributor.institution | Universidade Estadual de Campinas (UNICAMP) | |
dc.date.accessioned | 2014-05-27T11:25:28Z | |
dc.date.available | 2014-05-27T11:25:28Z | |
dc.date.issued | 2011-03-01 | |
dc.description.abstract | The simplest necessary conditions for an entire function ψ(x) =∞ ∑ k=0 γk xk/k! to be in the Laguerre-Pólya class are the Turán inequalities γ2 k- γk+1γk-1 ≥ 0. These are in fact necessary and sufficient conditions for the second degree generalized Jensen polynomials associated with ψ to be hyperbolic. The higher order Turán inequalities 4(γ2 n - γn-1γn+1)(γ2n +1 - γnγn+2) - (γnγn+1 - γn-1γn+2) 2 ≥ 0 are also necessary conditions for a function of the above form to belong to the Laguerre-Pólya class. In fact, these two sets of inequalities guarantee that the third degree generalized Jensen polynomials are hyperbolic. Pólya conjectured in 1927 and Csordas, Norfolk and Varga proved in 1986 that the Turán inequalities hold for the coefficients of the Riemann ψ-function. In this short paper, we prove that the higher order Turán inequalities also hold for the ψ-function, establishing the hyperbolicity of the associated generalized Jensen polynomials of degree three. © 2010 American Mathematical Society. | en |
dc.description.affiliation | Departamento de Ciências de Computação e Estatística IBILCE, Universidade Estadual Paulista, 15054-000 São José do Rio Preto, SP | |
dc.description.affiliation | Departamento de matemática Aplicada IMECC UNICAMP, 13083-859 Campinas, SP | |
dc.description.affiliationUnesp | Departamento de Ciências de Computação e Estatística IBILCE, Universidade Estadual Paulista, 15054-000 São José do Rio Preto, SP | |
dc.description.sponsorship | Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) | |
dc.description.sponsorship | Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) | |
dc.description.sponsorship | Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) | |
dc.description.sponsorshipId | FAPESP: 03/01874-2 | |
dc.description.sponsorshipId | FAPESP: 06/60420-0 | |
dc.description.sponsorshipId | CNPq: 305622/2009-9 | |
dc.description.sponsorshipId | CAPES: DGU-160 | |
dc.format.extent | 1013-1022 | |
dc.identifier | http://dx.doi.org/10.1090/S0002-9939-2010-10515-4 | |
dc.identifier.citation | Proceedings of the American Mathematical Society, v. 139, n. 3, p. 1013-1022, 2011. | |
dc.identifier.doi | 10.1090/S0002-9939-2010-10515-4 | |
dc.identifier.file | 2-s2.0-79951846250.pdf | |
dc.identifier.issn | 0002-9939 | |
dc.identifier.lattes | 1681267716971253 | |
dc.identifier.scopus | 2-s2.0-79951846250 | |
dc.identifier.uri | http://hdl.handle.net/11449/132295 | |
dc.identifier.wos | WOS:000288727900024 | |
dc.language.iso | eng | |
dc.publisher | Amer Mathematical Soc | |
dc.relation.ispartof | Proceedings of the American Mathematical Society | |
dc.relation.ispartofjcr | 0.707 | |
dc.relation.ispartofsjr | 1,183 | |
dc.rights.accessRights | Acesso aberto | |
dc.source | Scopus | |
dc.subject | Jensen polynomials | |
dc.subject | Laguerre-Pólya class | |
dc.subject | Maclaurin coefficients | |
dc.subject | Riemann ξ function | |
dc.subject | Turán inequalities | |
dc.title | Higher order turán inequalities for the Riemann ξ-function | en |
dc.type | Artigo | |
dcterms.license | http://www.ams.org/publications/authors/ctp | |
dcterms.rightsHolder | Amer Mathematical Soc | |
unesp.author.lattes | 1681267716971253 | |
unesp.campus | Universidade Estadual Paulista (Unesp), Instituto de Biociências Letras e Ciências Exatas, São José do Rio Preto | pt |
unesp.department | Ciências da Computação e Estatística - IBILCE | pt |
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