Involve: A Journal of Mathematics
- Volume 12, Number 5 (2019), 755-765.
The number of rational points of hyperelliptic curves over subsets of finite fields
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 nonresidues 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.
Involve, Volume 12, Number 5 (2019), 755-765.
Received: 19 January 2018
Revised: 21 June 2018
Accepted: 28 July 2018
First available in Project Euclid: 29 May 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Nelson, Kristina; Solymosi, József; Tom, Foster; Wong, Ching. The number of rational points of hyperelliptic curves over subsets of finite fields. Involve 12 (2019), no. 5, 755--765. doi:10.2140/involve.2019.12.755. https://projecteuclid.org/euclid.involve/1559095403