On quadratic progression sequences on smooth plane curves

Badr, Eslam and Sadek, Mohammad (2020) On quadratic progression sequences on smooth plane curves. Journal of Number Theory, 213 . pp. 445-452. ISSN 0022-314X (Print) 1096-1658 (Online)

[thumbnail of on_quadratic_progression_sequences_on_smooth_plane_curves.pdf] PDF
on_quadratic_progression_sequences_on_smooth_plane_curves.pdf
Restricted to Registered users only

Download (280kB) | Request a copy

Abstract

We study the arithmetic (geometric) progressions in the x-coordinates of quadratic points on smooth planar curves defined over a number field k. Unless the curve is hyperelliptic, we prove that these progressions must be finite. We, moreover, show that the arithmetic gonality of the curve determines the infinitude of these progressions in the set of k-points with field of definition of degree at most n, n >= 3.
Item Type: Article
Uncontrolled Keywords: Progression sequences; Smooth plane curves; Quadratic points; Bielliptic curves
Subjects: Q Science > QA Mathematics > QA150-272.5 Algebra
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: Mohammad Sadek
Date Deposited: 06 Sep 2020 09:19
Last Modified: 06 Sep 2020 09:19
URI: https://research.sabanciuniv.edu/id/eprint/40246

Actions (login required)

View Item
View Item