The smallest arithmetic hyperbolic three-orbifold

DOI10.1007/BF01389265zbMath0643.57011MaRDI QIDQ1102001

Ted Chinburg, Eduardo C. Friedman

Publication date: 1986

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143404

zbMATH Keywords

Coxeter grouphyperbolic 3-spacearithmetic subgroups of PSL(2,\({bbfC})\)complete, orientable, arithmetic hyperbolic 3-orbifold of minimal volumegroup of units in a maximal order in the Hamiltonian quaternion algebra

Mathematics Subject Classification ID

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Volumes of hyperbolic manifolds
• Arithmétique des algèbres de quaternions
• Ideale kleiner Norm in Idealklassen und eine Regulatorabschätzung
• Lower bounds for discriminants of number fields. II
• ON QUARTIC FIELDS OF SIGNATURE ONE WITH SMALL DISCRIMINANT
• A Lower Bound for the Volume of Hyperbolic 3-Manifolds
• The cusped hyperbolic 3-orbifold of minimum volume
• A Small Arithmetic Hyperbolic Three-Manifold
• Elastic waves in rods and clad rods
• Some analytic estimates of class numbers and discriminants

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