A lower bound concerning subset sums which do not cover all the residues modulo $p$.
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | DESHOUILLERS, Jean-Marc | |
| dc.date.accessioned | 2024-04-04T03:19:07Z | |
| dc.date.available | 2024-04-04T03:19:07Z | |
| dc.date.issued | 2005-01-01 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194476 | |
| dc.description.abstractEn | Let $c>\sqrt{2}$ and let $p$ be a prime number. J-M. Deshouillers and G. A. Freiman proved that a subset $\mathcal A$ of $\mathbb{Z}/p\mathbb{Z}$, with cardinality larger than $c\sqrt{p}$ and such that its subset sums do not cover $\mathbb{Z}/p\mathbb{Z}$ has an isomorphic image which is rather concentrated; more precisely, there exists $s$ prime to $p$ such that $$\sum_{a\in\mathcal A}\Vert\frac{as}{p}\Vert < 1+O(p^{-1/4}\ln p),$$ where the constant implied in the ``O'' symbol depends on $c$ at most. We show here that there exist a $K$ depending on $c$ at most, and such sets $\mathcal A$, such that for all $s$ prime to $p$ one has $$ \sum_{a\in\mathcal A}\Vert\frac{as}{p}\Vert>1+Kp^{-1/2}.$$ | |
| dc.language.iso | en | |
| dc.publisher | Hardy-Ramanujan Society | |
| dc.subject.en | upper bound for the error term | |
| dc.subject.en | residue classes modulo $p$ | |
| dc.title.en | A lower bound concerning subset sums which do not cover all the residues modulo $p$. | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.46298/hrj.2005.85 | |
| dc.subject.hal | Mathématiques [math] | |
| bordeaux.journal | Hardy-Ramanujan Journal | |
| bordeaux.page | 30-34 | |
| bordeaux.volume | Volume 28 - 2005 | |
| 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-01110947 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01110947v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Hardy-Ramanujan%20Journal&rft.date=2005-01-01&rft.volume=Volume%2028%20-%202005&rft.spage=30-34&rft.epage=30-34&rft.au=DESHOUILLERS,%20Jean-Marc&rft.genre=article |
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