Determinant Expressions for Hyperelliptic Functions in Genus Three

2001/05/23 by Yoshihiro Ônishi, Ônishi, Yoshihiro
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.math/0105187

AMS-TeX use 16 pages

openalex publication_date 2001/05/23 · arxiv created 2001/07/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we generalize the formula of Frobenius-Stickelberger and the formula of Kiepert to genus-three case. The latter is well-known determinant expression for any division polynomial of any elliptic curve.

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• Determinant Expressions for Hyperelliptic Functions (with an Appendix by Shigeki Matsutani)
• Determinant Expressions for Abelian Functions in Genus Two
• Differentiation of Genus 4 Hyperelliptic Functions
• The Problem of Differentiation of Hyperelliptic Functions
• Continued fractions and Hankel determinants from hyperelliptic curves