Generalizing Hurwitz’s quaternionic proof of Lagrange’s and Jacobi’s four-square theorems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10507683" target="_blank" >RIV/00216208:11320/25:10507683 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ClAQ4BMmR1" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ClAQ4BMmR1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.exmath.2025.125715" target="_blank" >10.1016/j.exmath.2025.125715</a>
Alternative languages
Result language
angličtina
Original language name
Generalizing Hurwitz’s quaternionic proof of Lagrange’s and Jacobi’s four-square theorems
Original language description
A proof of Lagrange’s and Jacobi’s four-square theorem due to Hurwitz utilizes orders in aquaternion algebra over the rationals. Seeking a generalization of this technique to orders overnumber fields, we identify two key components: an order with a good factorization theory andthe condition that all orbits under the action of the group of elements of norm 1 acting bymultiplication intersect the suborder corresponding to the quadratic form to be studied. We userecent results on class numbers of quaternion orders and then find all suborders satisfying the orbitcondition. Subsequently, we obtain universality and formulas for the number of representations bythe corresponding quadratic forms. We also present a quaternionic proof of Götzky’s four-squaretheorem.
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
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Expositiones Mathematicae
ISSN
0723-0869
e-ISSN
1878-0792
Volume of the periodical
43
Issue of the periodical within the volume
6
Country of publishing house
DE - GERMANY
Number of pages
45
Pages from-to
nestránkováno
UT code for WoS article
001542656700001
EID of the result in the Scopus database
2-s2.0-105011669882