Multiplicative relations among differences of singular moduli

verfasst von

Vahagn Aslanyan, Sebastian Eterović, Guy Fowler

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 \(n\).

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Typ

Preprint

Publikationsdatum

23.08.2023

Publikationsstatus

Elektronisch veröffentlicht (E-Pub)