On two-dimensional continued fractions for the integer hyperbolic matrices with small norm

Details On two-dimensional continued fractions for the integer hyperbolic matrices with small norm On two-dimensional continued fractions for the integer hyperbolic matrices with small norm

2009-11-16

arxiv.org/abs/0911.3040v1

Uspekhi Mat. Nauk 59 (2004), no. 5(359), 149--150; translation in Russian Math. Surveys 59 (2004), no. 5, 959--960

Mathematics

Number Theory

Scientific paper

10.1070/RM2004v059n05ABEH000778

In this note we classify two-dimensional continued fractions for cubic irrationalities constructed by matrices with not large norm ($|*| \le 6$). The classification is based on the following new result: the class of matrices with an irreducible characteristic polynomial over the field of rational numbers is the class of matrices of frobenius type iff there exists an integer solution for a certain equation with integer coefficients.

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