# Continued Fraction Approach to Gauss Reduction Theory

@inproceedings{Karpenkov2021ContinuedFA, title={Continued Fraction Approach to Gauss Reduction Theory}, author={O. N. Karpenkov}, booktitle={RP}, year={2021} }

Jordan Normal Forms serve as excellent representatives of conjugacy classes of matrices over closed fields. Once we knows normal forms, we can compute functions of matrices, their main invariant, etc. The situation is much more complicated if we search for normal forms for conjugacy classes over fields that are not closed and especially over rings. In this paper we study PGL(2,Z)-conjugacy classes of GL(2,Z) matrices. For the ring of integers Jordan approach has various limitations and in fact…

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