Computing Class Polynomials for Abelian Surfaces

DOI10.1080/10586458.2013.878675zbMath1293.11107arXiv1305.4330OpenAlexW2202985978MaRDI QIDQ2875530

Andreas Enge, Emmanuel Thomé

Publication date: 8 August 2014

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.4330

zbMATH Keywords

theta functionscomplex multiplicationalgebraic number theory computationsapplications to coding theory and cryptographyabelian varieties of dimension \(>1\)

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Theta functions and abelian varieties (14K25) Algebraic number theory computations (11Y40) Complex multiplication and abelian varieties (14K22) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (9)

Isogenous hyperelliptic and non-hyperelliptic Jacobians with maximal complex multiplication ⋮ A quasi-linear time algorithm for computing modular polynomials in dimension 2 ⋮ Hilbert theta series and invariants of genus 2 curves ⋮ Certified Newton schemes for the evaluation of low-genus theta functions ⋮ Computing Jacobi’s theta in quasi-linear time ⋮ Computing theta functions in quasi-linear time in genus two and above ⋮ Isogeny graphs of ordinary abelian varieties ⋮ Modular polynomials on Hilbert surfaces ⋮ Genus 3 hyperelliptic curves with CM via Shimura reciprocity

Cites Work

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• The complexity of class polynomial computation via floating point approximations
• Modern Computer Arithmetic
• Fast Multiple-Precision Evaluation of Elementary Functions
• Fast Decomposition of Polynomials with Known Galois Group
• On Siegel Modular Forms of Genus Two
• Computing Hilbert Class Polynomials
• The 2-Adic CM Method for Genus 2 Curves with Application to Cryptography

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