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Distribution of primes and approximation on weighted Dirichlet spaces

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dc.contributor.authorGallardo Gutiérrez, Eva A.
dc.contributor.authorSeco, Daniel
dc.date.accessioned2023-06-22T10:48:50Z
dc.date.available2023-06-22T10:48:50Z
dc.date.issued2022
dc.description.abstractWe study zero-free regions of the Riemann zeta function ζ related to an approximation problem in the weighted Dirichlet space D−2 which is known to be equivalent to the Riemann Hypothesis since the work of B ́aez-Duarte. We prove, indeed, that analogous approximation problems for the standard weighted Dirichlet spaces Dα when α ∈ (−3, −2) give conditions so that the half-plane {s ∈ C : R(s) > − α+12} is also zero-free for ζ. Moreover, we extend such results to a large family of weighted spaces of analytic functions lp α. As a particular instance, in the limit case p = 1 and α = −2, we provide a new proof of the Prime Number Theorem.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedFALSE
dc.description.sponsorshipMinisterio de Ciencia e Innovación (MICINN)
dc.description.sponsorshipCentro de Excelencia Severo Ochoa
dc.description.sponsorshipComunidad de Madrid / V PRICIT (Programa regional de Investigación y Innovación tecnológica
dc.description.statusunpub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/73278
dc.identifier.urihttps://hdl.handle.net/20.500.14352/71714
dc.language.isoeng
dc.relation.projectIDPID2019- 106433GB-I00;PID2019-105979GB-I00
dc.relation.projectIDCEX2019-000904-S
dc.relation.projectIDEPUC3M23
dc.rights.accessRightsopen access
dc.subject.cdu517
dc.subject.keywordRiemann zeta function
dc.subject.keywordweighted Dirichlet spaces
dc.subject.keywordcyclic vectors
dc.subject.ucmMatemáticas (Matemáticas)
dc.subject.ucmAnálisis matemático
dc.subject.unesco12 Matemáticas
dc.subject.unesco1202 Análisis y Análisis Funcional
dc.titleDistribution of primes and approximation on weighted Dirichlet spaces
dc.typejournal article
dspace.entity.typePublication
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