On quadratic Waring's problem in totally real number fields
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10472014" target="_blank" >RIV/00216208:11320/23:10472014 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=pw9Mfvvnk2" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=pw9Mfvvnk2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/proc/16233" target="_blank" >10.1090/proc/16233</a>
Alternative languages
Result language
angličtina
Original language name
On quadratic Waring's problem in totally real number fields
Original language description
We improve the bound of the g-invariant of the ring of integers of a totally real number field, where the g-invariant g(r) is the smallest num - ber of squares of linear forms in r variables that is required to represent all the quadratic forms of rank r that are representable by the sum of squares. Specifically, we prove that the gOK (r) of the ring of integers OK of a totally real number field K is at most gZ([K : Q]r). Moreover, it can also be bounded by gOF ([K : F]r + 1) for any subfield F of K. This yields a subexponential upper bound for g(r) of each ring of integers (even if the class number is not 1). Further, we obtain a more general inequality for the lattice version G(r) of the invariant and apply it to determine the value of G(2) for all but one real quadratic field.
Czech name
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Czech description
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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
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Proceedings of the American Mathematical Society
ISSN
0002-9939
e-ISSN
1088-6826
Volume of the periodical
151
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
15
Pages from-to
1471-1485
UT code for WoS article
000917020100001
EID of the result in the Scopus database
2-s2.0-85149247277