Computing Jacobi’s theta in quasi-linear time

DOI10.1090/mcom/3245zbMath1430.11167arXiv1511.04248OpenAlexW2962983176MaRDI QIDQ4605708

Hugo Labrande

Publication date: 27 February 2018

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

Full work available at URL: https://arxiv.org/abs/1511.04248

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Theta functions and abelian varieties (14K25) Computational aspects of algebraic curves (14Q05) Effectivity, complexity and computational aspects of algebraic geometry (14Q20) Software, source code, etc. for problems pertaining to number theory (11-04) Relationships between algebraic curves and physics (14H81) Theta functions and curves; Schottky problem (14H42)

Related Items (7)

Isogenous hyperelliptic and non-hyperelliptic Jacobians with maximal complex multiplication ⋮ Fast computation of the \(N\)-th term of a \(q\)-holonomic sequence and applications ⋮ Generators of the group of modular units for \(\Gamma^1(N)\) over the rationals ⋮ The Kullback-Leibler divergence between lattice Gaussian distributions ⋮ Certified Newton schemes for the evaluation of low-genus theta functions ⋮ Plane quartics over $\mathbb {Q}$ with complex multiplication ⋮ Modular polynomials on Hilbert surfaces

Uses Software

• MPC

Cites Work

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• The arithmetic-geometric mean of Gauss
• 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
• The complex AGM, periods of elliptic curves over \(\mathbb C\) and complex elliptic logarithms
• 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
• Gauss' algorithm revisited

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