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The number of
rational points of hyperelliptic curves over subsets of
finite fields
Kristina Nelson, József Solymosi, Foster Tom and Ching Wong
Vol. 12 (2019), No. 5, 755–765
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Abstract |
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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. |
Keywords
hyperelliptic curves, finite fields
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Mathematical Subject Classification 2010
Primary: 68Q87, 68R05
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Milestones
Received: 19 January 2018
Revised: 21 June 2018
Accepted: 28 July 2018
Published: 22 May 2019
Communicated by Kenneth S. Berenhaut
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Authors |
| Kristina Nelson | |
| Department of Mathematics University of California Berekeley, CA United States |
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| József Solymosi | |
| Department of Mathematics University of British Columbia Vancouver, BC Canada |
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| Foster Tom | |
| Department of Mathematics University of British Columbia Vancouver, BC Canada |
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| Ching Wong | |
| Department of Mathematics University of British Columbia Vancouver, BC Canada |
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