We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
LINEAR INDEPENDENCE OF POWERS OF SINGULAR MODULI OF DEGREE THREE.
- Authors
LUCA, FLORIAN; RIFFAUT, ANTONIN
- Abstract
We show that two distinct singular moduli $j(\unicode[STIX]{x1D70F}),j(\unicode[STIX]{x1D70F}^{\prime })$ , such that for some positive integers $m$ and $n$ the numbers $1,j(\unicode[STIX]{x1D70F})^{m}$ and $j(\unicode[STIX]{x1D70F}^{\prime })^{n}$ are linearly dependent over $\mathbb{Q}$ , 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.
- Subjects
MODULI theory; MATHEMATICS theorems; LOGARITHMS; LINEAR dependence (Mathematics); POLYNOMIALS
- Publication
Bulletin of the Australian Mathematical Society, 2019, Vol 99, Issue 1, p42
- ISSN
0004-9727
- Publication type
Article
- DOI
10.1017/S0004972718000965