Bounds for the Riemann zeta-function via Fourier analysis
Cotas para la función zeta de Riemann vía análisis de Fourier
| dc.contributor | Carneiro, Emanuel | |
| dc.creator | Chirre Chávez, Carlos Andrés | |
| dc.date | 2022-12-19T22:15:23Z | |
| dc.date | 2022-12-19T22:15:23Z | |
| dc.date | 2019 | |
| dc.date.accessioned | 2024-05-15T23:35:55Z | |
| dc.date.available | 2024-05-15T23:35:55Z | |
| dc.identifier | https://renati.sunedu.gob.pe/handle/sunedu/3335553 | |
| dc.identifier.uri | https://repositorioslatinoamericanos.uchile.cl/handle/2250/9452335 | |
| dc.description | En esta tesis se establecen nuevos límites para algunos objetos relacionados a la función zeta de Riemann y las L-funciones, bajo la hipótesis de Riemann, haciendo uso de maquinaria fina de teoría analítica de números, análisis harmónico y teoría de la aproximación. En particular, hacemos uso de aproximaciones de banda limitada, la reciente versión del método de resonancia dada por Kristian Seip y Andrii Bondarenko, y programación semidefinida. | |
| dc.description | In this Ph.D. thesis, we establish new bounds for some objects related to the Riemann zeta-function and L-functions, under the Riemann hypothesis, making use of ne tools from analytic number theory, harmonic analysis, and approximation theory. Firstly, we use extremal bandlimited approximations to show bounds for the high moments of the argument of the Riemann zeta-function and for a family of L-functions. Secondly, we use the resonance method of Soundararajan, in the version of Bondarenko and Seip, to obtain large values for the high moments of the argument function. Finally, we improve some estimates related with the distribution of the zeros of the Riemann zeta-function, using the approach of pair correlation of Montgomery and tools from semide nite programming. | |
| dc.description | Brasil. Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) (2015-2017) | |
| dc.description | Brasil. Fundação de Amparo à Pesquisa do Estado do Rio de Janeir (Faperj) (2017-2019) | |
| dc.format | application/pdf | |
| dc.format | application/pdf | |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Instituto de Matemática Pura e Aplicada | |
| dc.publisher | BR | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.rights | https://creativecommons.org/licenses/by/4.0/deed.es | |
| dc.source | Superintendencia Nacional de Educación Superior Universitaria - SUNEDU | |
| dc.source | Registro Nacional de Trabajos de Investigación - RENATI | |
| dc.subject | Hipótesis de Riemann | |
| dc.subject | Función zeta de Riemann | |
| dc.subject | Programación semidefinida | |
| dc.subject | https://purl.org/pe-repo/ocde/ford#1.01.00 | |
| dc.title | Bounds for the Riemann zeta-function via Fourier analysis | |
| dc.title | Cotas para la función zeta de Riemann vía análisis de Fourier | |
| dc.type | info:eu-repo/semantics/doctoralThesis |