Farei deries and continued fractions to the nearest even number

Abstract:

The evenness of the numerator and denominator of convergents of continued fraction to the nearest even number is opposite. We establish there that for nearly by 1=3 of almost all real numbers, convergents of its regular continued fraction expansion have either even numerator and odd denominator and eiter even denominator and odd numirator. This property holds for both
the lebesque measure just as for the distribution function of the so called Minkowski question mark function ?(x). Incindentally we establish that for
the measure that coresponds to the distribution ?(x), the mean of the n first elements of regular continued fraction tends to 2 as n tends to infinity.

Publication language:russian, страниц:12

Research direction:

Mathematical problems and theory of numerical methods