On the number of point of given order on odd degree hyperelliptic curves

2020/08/12 by John Boxall, Boxall, John
Computer Science · Mathematics · #11G20 #14H40 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2008.05253

openalex publication_date 2020/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For integers N≥ 3 and g≥ 1, 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.

Citations

• Courbes sur une vari�t� ab�lienne et points de torsion

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