• Corpus ID: 238856718

Bounds on entries in Bianchi group generators

@inproceedings{Martin2021BoundsOE,
  title={Bounds on entries in Bianchi group generators},
  author={Daniel Martin},
  year={2021}
}
Upper and lower bounds are given for the maximum Euclidean curvature among faces in Bianchi’s fundamental polyhedron for PSL2(O) in the upper-half space model of hyperbolic space, where O is an imaginary quadratic ring of integers with discriminant ∆. We prove these bounds are asymptotically within (log |∆|)8.54 of one another. This improves on the previous best upperbound, which is roughly off by a factor between |∆|2 and |∆|5/2 depending on the smallest prime dividing ∆. The gap between our… 

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References

SHOWING 1-10 OF 29 REFERENCES
Hyperbolic Tessellations Associated to Bianchi Groups
TLDR
This paper computes the structure of these polytopes for a range of imaginary quadratic fields using the model of positive definite binary Hermitian forms over F.
(Co)homologies and K-theory of Bianchi groups using computational geometric models
This thesis consists of the study of the geometry of a certain class of arithmetic groups, by means of a proper action on a contractible space. We will explicitly compute their group homology, and
Applications of a computer implementation of Poincaré’s theorem on fundamental polyhedra
PoincarCs Theorem asserts that a group F of isometries of hyperbolic space H is discrete if its generators act suitably on the boundary of some polyhedron in H, and when this happens a presentation
Modular symbols over number fields
Let K be a number field, R its ring of integers. For some classes of fields, spaces of cusp forms of weight 2 for GL(2;K) have been computed using methods based on modular symbols. J.E. Cremona [9]
Groups Acting on Hyperbolic Space: Harmonic Analysis and Number Theory
1. Three-Dimensional Hyperbolic Space.- 2. Groups Acting Discontinuously on Three-Dimensional Hyperbolic Space.- 3. Automorphic Functions.- 4. Spectral Theory of the Laplace Operator.- 5. Spectral
ON THE GROUP SL2 OVER DEDEKIND RINGS OF ARITHMETIC TYPE
It is proved that the group of matrices of order two with determinant 1 over a Dedekind ring of arithmetic type is generated by elementary matrices if there are infinitely many invertible elements in
Solution of the congruence subgroup problem for SLn (n ≥ 3) and Sp2n (n ≥ 2)
© Publications mathématiques de l’I.H.É.S., 1967, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://
Continued Fractions
The study of continued fractions is an ancient part of elementary Number Theory. It was studied by Leonhard Euler in the 18-th century. Actually, a remarkable paper from him was translated from Latin
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