Computing ideal classes representatives in quaternion algebras

DOI10.1090/S0025-5718-2014-02796-8zbMath1300.11117arXiv1007.2821OpenAlexW1979210277MaRDI QIDQ3189434

Nicolás Sirolli, Ariel Pacetti

Publication date: 10 September 2014

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

Full work available at URL: https://arxiv.org/abs/1007.2821

zbMATH Keywords

quaternion algebrastotally real number fieldideal classes

Mathematics Subject Classification ID

Quaternion and other division algebras: arithmetic, zeta functions (11R52)

Related Items (3)

Ideal classes of orders in quaternion algebras ⋮ Preimages for the Shimura map on Hilbert modular forms ⋮ On the change of root numbers under twisting and applications

Uses Software

• SageMath

Cites Work

• Unramified Hilbert modular forms, with examples relating to elliptic curves
• Shimura correspondence for level \(p^2\) and the central values of \(L\)-series
• On cubic rings and quaternion rings
• Arithmétique des algèbres de quaternions
• An algorithm for computing modular forms on \(\Gamma_0(N)\)
• On the arithmetic of quaternion algebras. II
• Corrigendum: Algorithmic Enumeration of Ideal Classes for Quaternion Orders
• On orders in quaternion algebras
• Class Groups, Totally Positive Units, and Squares
• On automorphisms of quaternion orders.
• A characterisation of Gorenstein orders in quarternition algebras.
• Simplification pour les ordres des corps de quaternions totalement définis.
• Computing weight $2$ modular forms of level $p^2$
• ARITHMETIC ON A QUINTIC THREEFOLD
• Computing Automorphic Forms on Shimura Curves over Fields with Arbitrary Class Number
• Advanced Topics in Computional Number Theory
• Computing Hilbert Modular Forms over Fields with Nontrivial Class Group
• Submodules of Quaternion Algebras

This page was built for publication: Computing ideal classes representatives in quaternion algebras