On the analogue of the division polynomials for hyperelliptic curves.

DOI10.1515/crll.1994.447.91zbMath0788.14026OpenAlexW133688896MaRDI QIDQ4279071

David G. Cantor

Publication date: 9 June 1994

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://www.digizeitschriften.de/dms/resolveppn/?PPN=GDZPPN002211343

zbMATH Keywords

Padé approximationszeta functiondivision polynomialsJacobian of a hyperelliptic curve

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Padé approximation (41A21) Elliptic curves (14H52) Jacobians, Prym varieties (14H40) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10)

Related Items (23)

Multiradical isogenies ⋮ A generalized Kiepert formula for \(C_{ab}\) curves ⋮ Sigma function solution of the initial value problem for Somos 5 sequences ⋮ Quasi-periodic and periodic solutions of the Toda lattice via the hyperelliptic sigma function ⋮ Modular equations for hyperelliptic curves ⋮ Improved complexity bounds for counting points on hyperelliptic curves ⋮ Genus 2 point counting over prime fields ⋮ Division polynomials and canonical local heights on hyperelliptic Jacobians ⋮ Efficient computation of Cantor's division polynomials of hyperelliptic curves over finite fields ⋮ Counting points on genus-3 hyperelliptic curves with explicit real multiplication ⋮ On the number of points of given order on odd-degree hyperelliptic curves ⋮ Average values on the Jacobian variety of a hyperelliptic curve ⋮ Towards a classification of entanglements of Galois representations attached to elliptic curves ⋮ One half log discriminant and division polynomials ⋮ Analytic solutions and integrability for bilinear recurrences of order six ⋮ The addition law attached to a stratification of a hyperelliptic Jacobian variety ⋮ Determinantal expressions for hyperelliptic functions in genus three ⋮ Division polynomials for hyperelliptic curves defined by Dickson polynomials ⋮ Counting points on hyperelliptic curves with explicit real multiplication in arbitrary genus ⋮ Recursion relation of hyperelliptic PSI-functions of genus two ⋮ Counting points on hyperelliptic curves of genus 2 with real models ⋮ Examples of torsion points on genus two curves ⋮ Elliptic and hyperelliptic solutions of discrete Painlevé I and its extensions to higher order difference equations

Cites Work

• Sequences of rational torsions on abelian varieties
• Sequences of numbers generated by addition in formal groups and new primality and factorization tests
• The Jacobian and formal group of a curve of genus 2 over an arbitrary ground field
• Elliptic Curves Over Finite Fields and the Computation of Square Roots mod p
• Arithmetic on curves
• Torsion points on elliptic curves over all quadratic fields. II
• Speeding the Pollard and Elliptic Curve Methods of Factorization
• Computing in the Jacobian of a Hyperelliptic Curve
• Computing Heights on Elliptic Curves
• Frobenius Maps of Abelian Varieties and Finding Roots of Unity in Finite Fields
• The Padé Table and Its Relation to Certain Algorithms of Numerical Analysis

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