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arXiv · 1710.02781

The number of rational points of hyperelliptic curves over subsets of finite fields

Kristina Nelson·Jozsef Solymosi·Foster Tom·Ching Wong
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Abstract

We prove two related concentration inequalities concerning the number of rational points of hyperelliptic curves over subsets of a finite field. In particular, we investigate the probability of a large discrepancy between the numbers of quadratic residues and non-residues in the image of such subsets over uniformly random hyperelliptic curves of given degrees. We find a constant probability of such a high difference and show the existence of sets with an exceptionally large discrepancy.

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Kristina Nelson, Jozsef Solymosi, Foster Tom, Ching Wong. 2017-10-08. The number of rational points of hyperelliptic curves over subsets of finite fields. https://arxiv.org/abs/1710.02781

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