• Corpus ID: 238856718

Bounds on entries in Bianchi group generators

  title={Bounds on entries in Bianchi group generators},
  author={Daniel Martin},
  • Daniel Martin
  • Published 13 October 2021
  • Mathematics
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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