Hilbert modular polynomials

DOI10.1016/j.jnt.2019.11.019zbMath1442.11171OpenAlexW2922059679MaRDI QIDQ2182178

Chloe Martindale

Publication date: 21 May 2020

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: http://www.martindale.info/research/hilbert.pdf

zbMATH Keywords

abelian varietiesgenus twocyclic isogeniesHilbert modular polynomialsmaximal real multiplication

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Abelian varieties of dimension (> 1) (11G10) Complex multiplication and moduli of abelian varieties (11G15) Isogeny (14K02)

Related Items (3)

Degree and height estimates for modular equations on PEL Shimura varieties ⋮ Computing square-free polarized abelian varieties over finite fields ⋮ Generalized class polynomials

Uses Software

• Magma
• Echidna

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Isogeny graphs of ordinary abelian varieties
• Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies
• Hilbertsche Modulformen und Modulfunktionen zu \({\mathbb{Q}}(\sqrt{5})\) (Hilbert modular forms and modular functions for \({\mathbb{Q}}(\sqrt{5})\))
• Hilbert theta series and invariants of genus 2 curves
• The Magma algebra system. I: The user language
• Towards practical key exchange from ordinary isogeny graphs
• CSIDH: an efficient post-quantum commutative group action
• Isogenies for point counting on genus two hyperelliptic curves with maximal real multiplication
• Hilbertsche Modulformen und Modulfunktionen zu \(Q(\sqrt{8})\)
• Counting points on elliptic curves over finite fields
• Quantum circuits for the CSIDH: optimizing quantum evaluation of isogenies
• Die Bestimmung der Funktionen zur Hilbertschen Modulgruppe des Zahlkörpers \(Q(\sqrt 5)\)
• Arithmetic variety of moduli for genus two
• Elliptic Modular Forms and Their Applications
• Computing modular polynomials in quasi-linear time
• Computing Hilbert class polynomials with the Chinese remainder theorem
• Modular Polynomials for Genus 2
• Counting Points on Genus 2 Curves with Real Multiplication
• A quasi-linear time algorithm for computing modular polynomials in dimension 2
• Frobenius Maps of Abelian Varieties and Finding Roots of Unity in Finite Fields
• On the compactification of arithmetically defined quotients of bounded symmetric domains

This page was built for publication: Hilbert modular polynomials