# 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…

## References

SHOWING 1-10 OF 29 REFERENCES

Hyperbolic Tessellations Associated to Bianchi Groups

- MathematicsANTS
- 2010

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

- Mathematics
- 2010

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

- Mathematics
- 1983

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

- Mathematics
- 2010

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

- Mathematics
- 1997

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

- Mathematics
- 1972

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)

- Mathematics
- 1967

© 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

- Education
- 1999

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…