Publikationsdetails
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
- Organisationseinheit(en)
-
Institut für Algebra, Zahlentheorie und Diskrete Mathematik
- Typ
- Artikel
- Journal
- Annali della Scuola normale superiore di Pisa - Classe di scienze
- ISSN
- 0391-173X
- Publikationsdatum
- 20.12.2024
- Publikationsstatus
- Elektronisch veröffentlicht (E-Pub)
- Elektronische Version(en)
-
https://doi.org/10.2422/2036-2145.202309_020 (Zugang:
Geschlossen
)
https://doi.org/10.48550/arXiv.2308.12244 (Zugang: Offen )
