Publication details
Multiplicative relations among differences of singular moduli
Abstract
Let \(n \in \mathbb{Z}_{>0}\). We prove that there exist a finite set \(V\) and finitely many algebraic curves \(T_1, \ldots, T_k\) with the following property: if \((x_1, \ldots, x_n, y)\) is an \((n+1)\)-tuple of pairwise distinct singular moduli such that \(\prod_{i=1}^n (x_i - y)^{a_i}=1\) for some \(a_1, \ldots, a_n \in \mathbb{Z} \setminus \{0\}\), then \((x_1, \ldots, x_n, y) \in V \cup T_1 \cup \ldots \cup T_k\). Further, the curves \(T_1, \ldots, T_k\) may be determined explicitly for a given \(n\).
Details
- Organisation(s)
-
Institute of Algebra, Number Theory and Discrete Mathematics
- Type
- Article
- Journal
- Annali della Scuola normale superiore di Pisa - Classe di scienze
- ISSN
- 0391-173X
- Publication date
- 20.12.2024
- Publication status
- E-pub ahead of print
- Electronic version(s)
-
https://doi.org/10.2422/2036-2145.202309_020 (Access:
Closed
)
https://doi.org/10.48550/arXiv.2308.12244 (Access: Open )
