Translator Disclaimer
2019 The number of rational points of hyperelliptic curves over subsets of finite fields
Kristina Nelson, József Solymosi, Foster Tom, Ching Wong
Involve 12(5): 755-765 (2019). DOI: 10.2140/involve.2019.12.755

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 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.

Citation

Download Citation

Kristina Nelson. József Solymosi. Foster Tom. Ching Wong. "The number of rational points of hyperelliptic curves over subsets of finite fields." Involve 12 (5) 755 - 765, 2019. https://doi.org/10.2140/involve.2019.12.755

Information

Received: 19 January 2018; Revised: 21 June 2018; Accepted: 28 July 2018; Published: 2019
First available in Project Euclid: 29 May 2019

zbMATH: 07072552
MathSciNet: MR3954294
Digital Object Identifier: 10.2140/involve.2019.12.755

Subjects:
Primary: 68Q87 , 68R05

Keywords: finite fields , hyperelliptic curves

Rights: Copyright © 2019 Mathematical Sciences Publishers

JOURNAL ARTICLE
11 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.12 • No. 5 • 2019
MSP
Back to Top