A cubic ring of integers with the smallest Pythagoras number

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10437977" target="_blank" >RIV/00216208:11320/22:10437977 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=vzxbShTHFL" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=vzxbShTHFL</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00013-021-01662-5" target="_blank" >10.1007/s00013-021-01662-5</a>

Result language
angličtina
Original language name
A cubic ring of integers with the smallest Pythagoras number
Original language description
We prove that the ring of integers in the totally real cubic subfield K-(49) of the cyclotomic field Q(zeta(7)) has Pythagoras number equal to 4. This is the smallest possible value for a totally real number field of odd degree. Moreover, we determine which numbers are sums of integral squares in this field, and use this knowledge to construct a diagonal universal quadratic form in five variables.
Czech name
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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
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GM21-00420M" target="_blank" >GM21-00420M: Universal Quadratic Forms and Class Numbers</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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