Papers › Effective multiplicative independence of 3 singular moduli
Effective multiplicative independence of 3 singular moduli
Yuri Bilu, Sanoli Gun, Emanuele Tron
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Pila and Tsimerman proved in 2017 that for every k there exists at most finitely many k-tuples (x₁,…, xₖ) of distinct non-zero singular moduli with the property "x₁, …,xₖ are multiplicatively dependent, but any proper subset of them is multiplicatively independent". The proof was non-effective, using Siegel's lower bound for the Class Number. In 2019 Riffaut obtained an effective version of this result for k=2. Moreover, he determined all the instances of xᵐyⁿ∈ℚ^×, where x,y are distinct singular moduli and m,n non-zero integers. In this article we obtain a similar result for k=3. We show that xᵐyⁿzʳ∈ℚ^× (where x,y,z are distinct singular moduli and m,n,r non-zero integers) implies that the discriminants of x,y,z do not exceed 10¹⁰.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections