Linear independence of powers of singular moduli of degree three
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F19%3AA20023MU" target="_blank" >RIV/61988987:17310/19:A20023MU - isvavai.cz</a>
Result on the web
<a href="https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/linear-independence-of-powers-of-singular-moduli-of-degree-three/A342A7350D6F9C18A4C53899F2187BCB#fndtn-information" target="_blank" >https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/linear-independence-of-powers-of-singular-moduli-of-degree-three/A342A7350D6F9C18A4C53899F2187BCB#fndtn-information</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S0004972718000965" target="_blank" >10.1017/S0004972718000965</a>
Alternative languages
Result language
angličtina
Original language name
Linear independence of powers of singular moduli of degree three
Original language description
We show that two distinct singular moduli j(tau), j(tau'), such that for some positive integers m and n the numbers 1, j(tau)(m) and j(tau')(n) are linearly dependent over Q, generate the same number field of degree at most two. This completes a result of Riffaut ['Equations with powers of singular moduli', Int. J. Number Theory, to appear], who proved the above theorem except for two explicit pairs of exceptions consisting of numbers of degree three. The purpose of this article is to treat these two remaining cases.
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/GA17-02804S" target="_blank" >GA17-02804S: Properties of number sequences and their applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
B AUST MATH SOC
ISSN
0004-9727
e-ISSN
—
Volume of the periodical
99
Issue of the periodical within the volume
1
Country of publishing house
GB - UNITED KINGDOM
Number of pages
9
Pages from-to
42-50
UT code for WoS article
000455194900006
EID of the result in the Scopus database
2-s2.0-85053119786