There are no universal ternary quadratic forms over biquadratic fields

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10414980" target="_blank" >RIV/00216208:11320/20:10414980 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=huvhD_fM1c" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=huvhD_fM1c</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S001309152000022X" target="_blank" >10.1017/S001309152000022X</a>

Result language
angličtina
Original language name
There are no universal ternary quadratic forms over biquadratic fields
Original language description
We study totally positive definite quadratic forms over the ring of integers O_K of a totally real biquadratic field K= Q(sqrt(m), sqrt(s)). We restrict our attention to classical forms (i.e., those with all non-diagonal coefficients in 2O_K) and prove that no such forms in three variables are universal (i.e., represent all totally positive elements of O_K). This provides further evidence towards Kitaoka's conjecture that there are only finitely many number fields over which such forms exist. One of our main tools are additively indecomposable elements of O_K; we prove several new results about their properties.
Czech name
—
Czech description
—

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
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)