On statistical properties of finite continued fractions.

Statistical properties of continued fractions for numbers a/b, where a and b lie in the sector a, b ≥ 1, a2 + b2 ≤ R2, are studied. The main result is an asymptotic formula with two meaning terms for the quantity where sx(a/b) = ¦{j ε {1, ..., s}: [0; tj, ..., ts] ≤ x}¦ is the Gaussian statistic for the fraction a/b = [t0; t1, ..., ts]. Bibliography: 12 titles. [ABSTRACT FROM AUTHOR]