Bolza Quaternion Order and Asymptotics of Systoles Along Congruence Subgroups

DOI10.1080/10586458.2015.1073642zbMath1411.11121arXiv1405.5454OpenAlexW2964128712MaRDI QIDQ5739439

Michael M. Schein, Uzi Vishne, Karin Usadi Katz, Mikhail G. Katz

Publication date: 15 July 2016

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.5454

zbMATH Keywords

ordertriangle groupsystolequaternion algebrahyperbolic surfacetotally real fieldprincipal congruence subgrouparithmetic Fuchsian groupinvariant trace fieldBolza curve

Mathematics Subject Classification ID

Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Finite-dimensional division rings (16K20) Quaternion and other division algebras: arithmetic, zeta functions (11R52)

Related Items (5)

Construction of hyperbolic Riemann surfaces with large systoles ⋮ Systolic length of triangular modular curves ⋮ Irreducible canonical representations in positive characteristic ⋮ An inequality for length and volume in the complex projective plane ⋮ Hyperbolic polyhedral surfaces with regular faces

Cites Work

• Hurwitz quaternion order and arithmetic Riemann surfaces
• Computing fundamental domains for Fuchsian groups
• Riemann surfaces with shortest geodesic of maximal length
• On the period matrix of a Riemann surface of large genus (with an appendix by J. H. Conway and N. J. A. Sloane)
• Systolic volume of homology classes
• Logarithmic growth of systole of arithmetic Riemann surfaces along congruence subgroups
• An optimal systolic inequality for \(\mathrm{CAT}(0)\) metrics in genus two
• Systole growth for finite area hyperbolic surfaces
• The Symmetry Type of a Riemann Surface
• Geometry of Riemann surfaces based on closed geodesics
• Dyck’s surfaces, systoles, and capacities

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