Lifting problem for universal quadratic forms

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10438405" target="_blank" >RIV/00216208:11320/21:10438405 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=On3SHHrZRP" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=On3SHHrZRP</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aim.2020.107497" target="_blank" >10.1016/j.aim.2020.107497</a>

Result language
angličtina
Original language name
Lifting problem for universal quadratic forms
Original language description
We study totally real number fields that admit a universal quadratic form whose coefficients are rational integers. We show that Q(root 5) is the only such real quadratic field, and that among fields of degrees 3, 4, 5, and 7 which have principal codifferent ideal, the only one is Q(zeta(7) + zeta(-1)(7)), over which the form x(2) + y(2) + z(2) + w(2) + xy + xz + xw is universal. Moreover, we prove an upper bound for Pythagoras numbers of orders in number fields that depends only on the degree of the number field. (C) 2020 Elsevier Inc. All rights reserved.
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/GJ17-04703Y" target="_blank" >GJ17-04703Y: Quadratic forms and numeration systems over number fields</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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