Small diameters and generators for arithmetic lattices in SL₂(R) and certain Ramanujan graphs
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Date
2023-12
Publication Type
Journal Article
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yes
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Abstract
We show that arithmetic lattices in SL₂(R), stemming from the proper units of an Eichler order in an indefinite quaternion algebra over Q, admit a 'small' covering set. In particular, we give bounds on the diameter if the quotient space is co-compact. Consequently, we show that these lattices admit small generators. Our techniques also apply to definite quaternion algebras where we show Ramanujan-strength bounds on the diameter of certain Ramanujan graphs without the use of the Ramanujan bound.
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published
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Journal / series
Volume
62 (4)
Pages / Article No.
953 - 966
Publisher
Springer
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Edition / version
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Software
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Date collected
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Subject
Diameter; Size of generators; Fuchsian groups; Arithmetic hyperbolic surface; Ramanujan graph
Organisational unit
02000 - Dep. Mathematik / Dep. of Mathematics