Certified Newton schemes for the evaluation of low-genus theta functions

DOI10.1007/s11075-022-01443-3arXiv2203.02000OpenAlexW4312064046MaRDI QIDQ6157454

Jean Kieffer

Publication date: 11 May 2023

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.02000

zbMATH Keywords

Newton's methodtheta functionsrigorous computationsgenus 2

Mathematics Subject Classification ID

Numerical analysis (65-XX) Combinatorics (05-XX)

Cites Work

• Higher genus arithmetic-geometric means
• The arithmetic-geometric mean of Gauss
• Computing theta functions with Julia
• Efficient computation of multidimensional theta functions
• Computing Igusa class polynomials
• Computing Class Polynomials for Abelian Surfaces
• Computing theta functions in quasi-linear time in genus two and above
• Fast evaluation of modular functions using Newton iterations and the AGM
• The complexity of class polynomial computation via floating point approximations
• Computing modular polynomials in quasi-linear time
• Computing Jacobi’s theta in quasi-linear time
• Short addition sequences for theta functions
• Computing Riemann theta functions
• On the variety associated to the ring of theta constants in genus 3
• Fast genus 2 arithmetic based on Theta functions
• On the Graded Ring of Theta-Constants
• Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura
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