Additive properties of sequences of pseudo $s$-th powers
| hal.structure.identifier | Departamento de Matemáticas [Madrid] | |
| dc.contributor.author | CILLERUELO, Javier | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | DESHOUILLERS, Jean-Marc | |
| hal.structure.identifier | Centre de Mathématiques Laurent Schwartz [CMLS] | |
| dc.contributor.author | LAMBERT, Victor | |
| hal.structure.identifier | Centre de Mathématiques Laurent Schwartz [CMLS] | |
| dc.contributor.author | PLAGNE, Alain | |
| dc.date.accessioned | 2024-04-04T03:20:24Z | |
| dc.date.available | 2024-04-04T03:20:24Z | |
| dc.date.created | 2014-07-20 | |
| dc.date.issued | 2016 | |
| dc.identifier.issn | 0025-5874 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194584 | |
| dc.description.abstractEn | In this paper, we study (random) sequences of pseudo s-th powers, as introduced by Erdös and Rényi in 1960. In 1975, Goguel proved that such a sequence is almost surely not an asymptotic basis of order s. Our first result asserts that it is however almost surely a basis of order s + x for any x > 0. We then study the s-fold sumset sA = A + ... + A (s times) and in particular the minimal size of an additive complement, that is a set B such that sA + B contains all large enough integers. With respect to this problem, we prove quite precise theorems which are tantamount to asserting that a threshold phenomenon occurs. | |
| dc.language.iso | en | |
| dc.publisher | Springer | |
| dc.title.en | Additive properties of sequences of pseudo $s$-th powers | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s00209-016-1651-8 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 1407.5291 | |
| bordeaux.journal | Mathematische Zeitschrift | |
| bordeaux.page | 175-193 | |
| bordeaux.volume | 284 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01074153 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01074153v1 | |
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