| dc.contributor.author | Jiménez Urroz, Jorge |
| dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
| dc.date.accessioned | 2022-04-12T09:49:56Z |
| dc.date.issued | 2021-12-30 |
| dc.identifier.citation | Jimenez, J. Every integer can be written as a square plus a squarefree. "Expositiones mathematicae", 30 Desembre 2021, |
| dc.identifier.issn | 0723-0869 |
| dc.identifier.other | https://arxiv.org/abs/2010.15580 |
| dc.identifier.uri | http://hdl.handle.net/2117/365735 |
| dc.description | © 2021 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| dc.description.abstract | In the paper we can prove that every integer can be written as the sum of two integers, one perfect square and one squarefree. We also establish the asymptotic formula for the number of representations of an integer in this form. The result is deeply related with the divisor function. In the course of our study we get an independent result about it. Concretely we are able to deduce a new upper bound for the divisor function fully explicit. |
| dc.language.iso | eng |
| dc.rights | ©2021. Elsevier |
| dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ |
| dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres |
| dc.subject.lcsh | Multiplicity (Mathematics) |
| dc.subject.lcsh | Partitions (Mathematics) |
| dc.subject.other | Additive number theory |
| dc.subject.other | Arithmetic functions |
| dc.subject.other | Divisor function |
| dc.title | Every integer can be written as a square plus a squarefree |
| dc.type | Article |
| dc.subject.lemac | Nombres, Teoria dels |
| dc.subject.lemac | Particions (Matemàtica) |
| dc.contributor.group | Universitat Politècnica de Catalunya. TN - Grup de Recerca en Teoria de Nombres |
| dc.identifier.doi | 10.1016/j.exmath.2021.12.002 |
| dc.description.peerreviewed | Peer Reviewed |
| dc.subject.ams | Classificació AMS::11 Number theory::11N Multiplicative number theory |
| dc.subject.ams | Classificació AMS::11 Number theory::11P Additive number theory; partitions |
| dc.relation.publisherversion | https://www.sciencedirect.com/science/article/abs/pii/S0723086921000748 |
| dc.rights.access | Restricted access - publisher's policy |
| local.identifier.drac | 32580219 |
| dc.description.version | Postprint (author's final draft) |
| dc.date.lift | 2023-12-30 |
| local.citation.author | Jimenez, J. |
| local.citation.publicationName | Expositiones mathematicae |
