# 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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