April 2023 ON THE NUMBER OF POINTS OF GIVEN ORDER ON ODD-DEGREE HYPERELLIPTIC CURVES
John Boxall
Rocky Mountain J. Math. 53(2): 357-382 (April 2023). DOI: 10.1216/rmj.2023.53.357

Abstract

For integers N2 and g1, we study bounds on the cardinality of the set of points of order dividing N lying on a hyperelliptic curve of genus g embedded in its jacobian using a Weierstrass point as base point. This leads us to revisit division polynomials introduced by Cantor in 1995 and strengthen a divisibility result proved by him. Several examples are discussed.

Citation

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John Boxall. "ON THE NUMBER OF POINTS OF GIVEN ORDER ON ODD-DEGREE HYPERELLIPTIC CURVES." Rocky Mountain J. Math. 53 (2) 357 - 382, April 2023. https://doi.org/10.1216/rmj.2023.53.357

Information

Received: 3 December 2020; Revised: 14 June 2022; Accepted: 21 June 2022; Published: April 2023
First available in Project Euclid: 20 June 2023

MathSciNet: MR4604761
zbMATH: 07725142
Digital Object Identifier: 10.1216/rmj.2023.53.357

Subjects:
Primary: 14H40 , 14H45
Secondary: 14G17

Keywords: hyperelliptic curves , Jacobian varieties , torsion points

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

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Vol.53 • No. 2 • April 2023
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