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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)

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Official URL: http://dx.doi.org/10.1016/j.jnt.2019.12.018

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
ID Code:40246
Deposited By:Mohammad Sadek
Deposited On:06 Sep 2020 09:19
Last Modified:06 Sep 2020 09:19

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