Computing theta functions in quasi-linear time in genus two and above

DOI10.1112/S1461157016000309zbMath1361.14028OpenAlexW2509268339MaRDI QIDQ2971008

Hugo Labrande, Emmanuel Thomé

Publication date: 4 April 2017

Published in: LMS Journal of Computation and Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/s1461157016000309

zbMATH Keywords

theta functions

Mathematics Subject Classification ID

Theta functions and abelian varieties (14K25) Theta functions and curves; Schottky problem (14H42)

Related Items (6)

Fast computation of the \(N\)-th term of a \(q\)-holonomic sequence and applications ⋮ Certified Newton schemes for the evaluation of low-genus theta functions ⋮ On computing high-dimensional Riemann theta functions ⋮ An inverse Jacobian algorithm for Picard curves ⋮ Plane quartics over $\mathbb {Q}$ with complex multiplication ⋮ Modular polynomials on Hilbert surfaces

Cites Work

• Explizite Bestimmung der Randflächen des Fundamentalbereiches der Modulgruppe zweiten Grades
• Algorithms to construct Minkowski reduced and Hermite reduced lattice bases
• Tata lectures on theta. I: Introduction and motivation: Theta functions in one variable. Basic results on theta functions in several variables. With the assistance of C. Musili, M. Nori, E. Previato, and M. Stillman
• Computing Class Polynomials for Abelian Surfaces
• Fast evaluation of modular functions using Newton iterations and the AGM
• The complexity of class polynomial computation via floating point approximations
• Equations for the Jacobian of a hyperelliptic curve
• Computing Riemann theta functions

This page was built for publication: Computing theta functions in quasi-linear time in genus two and above