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The number of rational points of hyperelliptic curves over subsets of finite fields (1710.02781v2)

Published 8 Oct 2017 in cs.CR and math.NT

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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