Artykuł
Geometric properties of the lattice of polynomials with integer coefficients
| creativeworkseries.issn | 1232-9274 | |
| dc.contributor.author | Lipnicki, Artur | |
| dc.contributor.author | Śmietański, Marek J. | |
| dc.date.issued | 2024 | |
| dc.description.abstract | This paper is related to the classic but still being examined issue of approximation of functions by polynomials with integer coefficients. Let $r$, $n$ be positive integers with $n \ge 6r$. Let $\boldsymbol{P}_n \cap \boldsymbol{M}_r$ be the space of polynomials of degree at most $n$ on $[0,1]$ with integer coefficients such that $P^{(k)}(0)/k!$ and $P^{(k)}(1)/k!$ are integers for $k=0,\dots,r-1$ and let $\boldsymbol{P}_n^\mathbb{Z} \cap \boldsymbol{M}_r$ be the additive group of polynomials with integer coefficients. We explore the problem of estimating the minimal distance of elements of $\boldsymbol{P}_n^\mathbb{Z} \cap \boldsymbol{M}_r$ from $\boldsymbol{P}_n \cap \boldsymbol{M}_r$ in $L_2(0,1)$. We give rather precise quantitative estimations for successive minima of $\boldsymbol{P}_n^\mathbb{Z}$ in certain specific cases. At the end, we study properties of the shortest polynomials in some hyperplane in $\boldsymbol{P}_n \cap \boldsymbol{M}_r$. | en |
| dc.description.placeOfPublication | Kraków | |
| dc.description.version | wersja wydawnicza | |
| dc.identifier.doi | https://doi.org/10.7494/OpMath.2024.44.4.565 | |
| dc.identifier.eissn | 2300-6919 | |
| dc.identifier.issn | 1232-9274 | |
| dc.identifier.uri | https://repo.agh.edu.pl/handle/AGH/108414 | |
| dc.language.iso | eng | |
| dc.publisher | Wydawnictwa AGH | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.access | otwarty dostęp | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/legalcode | |
| dc.subject | approximation by polynomials with integer coefficients | en |
| dc.subject | lattice | en |
| dc.subject | covering radius | en |
| dc.subject | roots of polynomial | en |
| dc.title | Geometric properties of the lattice of polynomials with integer coefficients | en |
| dc.title.related | Opuscula Mathematica | |
| dc.type | artykuł | |
| dspace.entity.type | Publication | |
| publicationissue.issueNumber | No. 4 | |
| publicationissue.pagination | pp. 565-585 | |
| publicationvolume.volumeNumber | Vol. 44 | |
| relation.isJournalIssueOfPublication | 958a565f-0ba8-4db5-bbd6-a87484b6015d | |
| relation.isJournalIssueOfPublication.latestForDiscovery | 958a565f-0ba8-4db5-bbd6-a87484b6015d | |
| relation.isJournalOfPublication | 304b3b9b-59b9-4830-9178-93a77e6afbc7 |
Pliki
Pakiet podstawowy
1 - 1 z 1
Ładuję...
- Nazwa:
- OpMath.2024.44.4.565.pdf
- Rozmiar:
- 642.24 KB
- Format:
- Adobe Portable Document Format
- Opis: