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Collinear CM-points

Bilu, Yuri and Luca, Florina and Masser, David. (2017) Collinear CM-points. Preprints Fachbereich Mathematik, 2017 (03).

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Abstract

André’s celebrated Theorem of 1998 implies that each complex straight line Ax + By + C = 0 (apart from obvious exceptions) contains at most finitely many points $(j(\tau),j(\tau^\prime))$, where $\tau, \tau^\prime \in \mathbb{H}$ are algebraic of degree 2. We show that there are only a finite number of such lines which contain more than two such points. As there is a line through any two complex points, this is best possible.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Zahlentheorie (Masser)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Masser, David
Item Type:Preprint
Publisher:Universität Basel
Language:English
Last Modified:17 Apr 2019 19:58
Deposited On:28 Mar 2019 09:51

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