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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

  • Czech description

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/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