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A computational method for the construction of Siegel sets in complex hyperbolic space

Tyler, B.M.; (2010) A computational method for the construction of Siegel sets in complex hyperbolic space. Doctoral thesis, UCL (University College London). Green open access

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Abstract

This thesis presents a computational method for constructing Siegel sets for the action of \Gamma = SU(n; 1;O) on HnC, where O is the ring of integers of an imaginary quadratic field with trivial class group. The thesis first presents a basic algorithm for computing Siegel sets and then considers practical improvements which can be made to this algorithm in order to decrease computation time. This improved algorithm is implemented in a C++ program called siegel, the source code for which is freely available at http://code.google.com/p/siegel/, and this program is used to compute explicit Siegel sets for the action of all applicable groups \Gamma on H2C and H3C.

Type: Thesis (Doctoral)
Title: A computational method for the construction of Siegel sets in complex hyperbolic space
Open access status: An open access version is available from UCL Discovery
Language: English
Additional information: The abstract contains LaTeX text. Please see the attached pdf for rendered equations
UCL classification: UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics
URI: http://discovery.ucl.ac.uk/id/eprint/147750
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