Ternary quadratic forms representing a given arithmetic progression
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60461373%3A22340%2F22%3A43934053" target="_blank" >RIV/60461373:22340/22:43934053 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/22:10453499
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0022314X21003310" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022314X21003310</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jnt.2021.09.017" target="_blank" >10.1016/j.jnt.2021.09.017</a>
Alternative languages
Result language
angličtina
Original language name
Ternary quadratic forms representing a given arithmetic progression
Original language description
A positive quadratic form is (k,ℓ)-universal if it represents all the numbers kx+ℓ where x is a non-negative integer, and almost (k,ℓ)-universal if it represents all but finitely many of them. We prove that for any k,ℓ such that k∤ℓ there exists an almost (k,ℓ)-universal diagonal ternary form. We also conjecture that there are only finitely many primes p for which a (p,ℓ)-universal diagonal ternary form exists (for any ℓ<p) and we show the results of computer experiments that speak in favor of the conjecture. © 2021 Elsevier Inc.
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
10100 - Mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
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
JOURNAL OF NUMBER THEORY
ISSN
0022-314X
e-ISSN
1096-1658
Volume of the periodical
234
Issue of the periodical within the volume
October
Country of publishing house
US - UNITED STATES
Number of pages
13
Pages from-to
140-152
UT code for WoS article
000795908300007
EID of the result in the Scopus database
2-s2.0-85118261273