On determination of periods of geometric continued fractions for two-dimensional algebraic hyperbolic operators

2007/08/12 by O. Karpenkov, Karpenkov, O.
Mathematics · #11J70 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11J70

paper · pdf · doi:10.48550/arxiv.0708.1604

arxiv created 2007/08/12 · arxiv updated 2009/12/01

Abstract

For a given sequence of positive integers we make an explicit construction of a reduced hyperbolic operator in SL(2,z) with the sequence as a period of a geometric continued fraction in the sense of Klein. Further we experimentally study an algorithm to construct a period for an arbitrary operator of SL(2,z) (the Gauss Reduction Theory).

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