Determination of Periods of Geometric Continued Fractions for Two-Dimensional Algebraic Hyperbolic Operators

作者：Karpenkov O N^*

来源：Mathematical Notes, 2010, 88(1-2): 28-38.

DOI：10.1134/S0001434610070035

• geometric continued fraction in the sense of Klein
• period of a geometric continued fraction
• hyperbolic integer operator
• sail of an integer operator
• LLS-sequence
• integer length
• integer sine

An explicit construction of a reduced hyperbolic integer operator from the group SL(2, Z) such that one of the periods of the corresponding geometric continued fraction in the sense of Klein coincides with a given sequence of positive integers is presented. An algorithm determining periods for any operator in SL(2, Z) (which is based on Gauss' reduction theory) is experimentally studied.

• 出版日期2010-8