In this paper, we study the finiteness problem of torsion points on an elliptic curve whose coordinates satisfy some multiplicative dependence relations. In particular, we prove that on an elliptic curve defined over a number field there are only finitely many torsion points whose coordinates are multiplicatively dependent. Moreover, we produce an effective result when the elliptic curve is defined over the rational numbers or has complex multiplication.
Barroero, F., Sha, M. (2020). TORSION POINTS WITH MULTIPLICATIVELY DEPENDENT COORDINATES ON ELLIPTIC CURVES. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 52(5), 807-815 [10.1112/blms.12363].
TORSION POINTS WITH MULTIPLICATIVELY DEPENDENT COORDINATES ON ELLIPTIC CURVES
FABRIZIO BARROERO;
2020-01-01
Abstract
In this paper, we study the finiteness problem of torsion points on an elliptic curve whose coordinates satisfy some multiplicative dependence relations. In particular, we prove that on an elliptic curve defined over a number field there are only finitely many torsion points whose coordinates are multiplicatively dependent. Moreover, we produce an effective result when the elliptic curve is defined over the rational numbers or has complex multiplication.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
