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