Multiplicative dependence in the denominators of points of elliptic curves
Abstract
Abstract Let $$E_1, \ldots , E_s $$ E 1 , … , E s be s , not necessary distinct, elliptic curves over $${\mathbb {Q}}$$ Q . We give upper bounds on the frequency of s -tuples of points in $$E_1({\mathbb {Q}})\times \ldots \times E_s({\mathbb {Q}})$$ E 1 ( Q ) × … × E s ( Q ) whose denominators or x -coordinates are multiplicatively dependent. More precisely, we give such bounds in two scenarios: one in which we fix s non-torsion $${\mathbb {Q}}$$ Q -rational points $$P_i \in E_i({\mathbb {Q}})$$ P i ∈ E i ( Q ) and arbitrary $${\mathbb {Q}}$$ Q -rational points $$Q_i \in E_i({\mathbb {Q}})$$ Q i ∈ E i ( Q ) , $$i =1, \ldots , s$$ i = 1 , … , s , and we count s -tuples $$ (n_1P_1+Q_1,\ldots , n_sP_s+Q_s) \in E_1({\mathbb {Q}}) \times \ldots \times E_s({\mathbb {Q}}) $$ ( n 1 P 1 + Q 1 , … , n s P s + Q s ) ∈ E 1 ( Q ) × … × E
Fields of Study & Subjects
advanced mathematical theories
Algebraic Geometry and Number Theory
Analytic Number Theory Research
Publication details
- Journal / source
- Monatshefte für Mathematik
- Publisher
- Springer Science and Business Media LLC
- Volume
- 211
- Issue
- 1
- Pages
- 25–45
- Publication date
- 16 July 2026
- Language
- EN