Publication: Distribution of primes and approximation on weighted Dirichlet spaces
dc.contributor.author | Gallardo Gutiérrez, Eva A. | |
dc.contributor.author | Seco, Daniel | |
dc.date.accessioned | 2023-06-22T10:48:50Z | |
dc.date.available | 2023-06-22T10:48:50Z | |
dc.date.issued | 2022 | |
dc.description.abstract | We 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.department | Depto. de Análisis Matemático y Matemática Aplicada | |
dc.description.faculty | Fac. de Ciencias Matemáticas | |
dc.description.refereed | FALSE | |
dc.description.sponsorship | Ministerio de Ciencia e Innovación (MICINN) | |
dc.description.sponsorship | Centro de Excelencia Severo Ochoa | |
dc.description.sponsorship | Comunidad de Madrid / V PRICIT (Programa regional de Investigación y Innovación tecnológica | |
dc.description.status | unpub | |
dc.eprint.id | https://eprints.ucm.es/id/eprint/73278 | |
dc.identifier.uri | https://hdl.handle.net/20.500.14352/71714 | |
dc.language.iso | eng | |
dc.relation.projectID | PID2019- 106433GB-I00;PID2019-105979GB-I00 | |
dc.relation.projectID | CEX2019-000904-S | |
dc.relation.projectID | EPUC3M23 | |
dc.rights.accessRights | open access | |
dc.subject.cdu | 517 | |
dc.subject.keyword | Riemann zeta function | |
dc.subject.keyword | weighted Dirichlet spaces | |
dc.subject.keyword | cyclic vectors | |
dc.subject.ucm | Matemáticas (Matemáticas) | |
dc.subject.ucm | Análisis matemático | |
dc.subject.unesco | 12 Matemáticas | |
dc.subject.unesco | 1202 Análisis y Análisis Funcional | |
dc.title | Distribution of primes and approximation on weighted Dirichlet spaces | |
dc.type | journal article | |
dspace.entity.type | Publication |
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