@techreport{e135dba679eb41969d72d166f62614e8, title = "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 \(n\). ", keywords = "math.NT", author = "Vahagn Aslanyan and Sebastian Eterovi{\'c} and Guy Fowler", note = "36 pages", year = "2023", month = aug, day = "23", doi = "10.48550/arXiv.2308.12244", language = "English", type = "WorkingPaper", }