Indecomposable integers in real quadratic fields
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10414274" target="_blank" >RIV/00216208:11320/20:10414274 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=nXIJdz3_fp" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=nXIJdz3_fp</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jnt.2019.11.005" target="_blank" >10.1016/j.jnt.2019.11.005</a>
Alternative languages
Result language
angličtina
Original language name
Indecomposable integers in real quadratic fields
Original language description
In 2016, Jang and Kim stated a conjecture about the norms of indecomposable integers in real quadratic number fields Q (root D) where D > 1 is a squarefree integer. Their conjecture was later disproved by Kala for D 2 mod 4. We investigate such indecomposable integers in greater detail. In particular, we find the minimal D in each congruence class D 1, 2,3 mod 4 that provides a counterexample to the Jang-Kim Conjecture; provide infinite families of such counterexamples; and state a refined version of the Jang-Kim Conjecture. Lastly, we prove a slightly weaker version of our refined conjecture that is of the correct order of magnitude, showing the Jang-Kim Conjecture is only wrong by at most O (root D). (C) 2019 Elsevier Inc. All rights reserved.
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
<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)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Number Theory
ISSN
0022-314X
e-ISSN
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Volume of the periodical
212
Issue of the periodical within the volume
July 2020
Country of publishing house
US - UNITED STATES
Number of pages
25
Pages from-to
458-482
UT code for WoS article
000523512000021
EID of the result in the Scopus database
2-s2.0-85077147715