STATISTICAL-MECHANICAL METHODS AND CONTINUED FRACTIONS

For a(1), ..., a(n) a finite sequence of strictly positive integers, w e denote by q(n)(a(1), ..., a(n)) the denominator of the finite contin ued fraction [a(1), ..., a(n)] written as a quotient of two relatively prime integers. We show that the sequence of functions log q(n)(a(1), ..., a(n)), n = 1, 2, ..., have the formal properties of a Hamiltonia n for a one-dimensional lattice system, to which the methods of statis tical mechanics can be applied, and we investigate the properties of t he system so defined.