Geometriae Dedicata

, Volume 155, Issue 1, pp 151–161 | Cite as

Hurwitz quaternion order and arithmetic Riemann surfaces

  • Mikhail G. KatzEmail author
  • Mary Schaps
  • Uzi Vishne
Original Paper


We clarify the explicit structure of the Hurwitz quaternion order, which is of fundamental importance in Riemann surface theory and systolic geometry.


Arithmetic lattice Azumaya algebras Fuchsian group Hurwitz group Hurwitz order Hyperbolic surface Hyperbolic reflection group Quaternion algebra Subgroup growth Systole 

Mathematics Subject Classification (2000)

11R52 53C23 16K20 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of MathematicsBar Ilan UniversityRamat GanIsrael

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