Arithmetic of cubic number fields: Jacobi-Perron, Pythagoras, and indecomposables

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10508569" target="_blank" >RIV/00216208:11320/25:10508569 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21240/25:00381953
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=_esQpRGh5q" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=_esQpRGh5q</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jnt.2024.12.001" target="_blank" >10.1016/j.jnt.2024.12.001</a>

Result language
angličtina
Original language name
Arithmetic of cubic number fields: Jacobi-Perron, Pythagoras, and indecomposables
Original language description
We study a new connection between multidimensional continued fractions, such as Jacobi-Perron algorithm, and additively indecomposable integers in totally real cubic number fields. First, we find the indecomposables of all signatures in Ennola's family of cubic fields, and use them to determine the Pythagoras numbers. Second, we compute a number of periodic JPA expansions, also in Shanks' family of simplest cubic fields. Finally, we compare these expansions with indecomposables to formulate our conclusions.<br /> (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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