Computing Cantor division polynomials via differential equations

Abstract: The computation of Cantor division polynomials is an essential step in Pila's algorithm for counting points on hyperelliptic curves and their Jacobians over finite fields. Classical algorithms for computing these polynomials are usually based on Cantor’s recurrence formulas and Cantor’s algorithm for adding points on Jacobians. Although, they exhibit acceptable running time in practice, their theoretical complexity has not been well studied yet and experiments show that they become much slower when the degree or the genus get higher. In this talk, I will provide an efficient way to calculate them, based on solving some non-linear differential equations.

algebraic geometrynumber theory

Audience: researchers in the topic

Leiden Algebra, Geometry, and Number Theory Seminar