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A cubic ring of integers with the smallest Pythagoras number

The result's identifiers

  • 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>

Alternative languages

  • 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

  • Czech description

Classification

  • 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

Result continuities

  • 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)

Others

  • Publication year

    2022

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Archiv der Mathematik

  • ISSN

    0003-889X

  • e-ISSN

    1420-8938

  • Volume of the periodical

    2021

  • Issue of the periodical within the volume

    118

  • Country of publishing house

    CH - SWITZERLAND

  • Number of pages

    10

  • Pages from-to

    39-48

  • UT code for WoS article

    000709235300001

  • EID of the result in the Scopus database

    2-s2.0-85117362493