Involve: A Journal of Mathematics

  • Involve
  • Volume 12, Number 5 (2019), 755-765.

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

Kristina Nelson, József Solymosi, Foster Tom, and Ching Wong

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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.

Article information

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 68Q87: Probability in computer science (algorithm analysis, random structures, phase transitions, etc.) [See also 68W20, 68W40] 68R05: Combinatorics

hyperelliptic curves finite fields


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.

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