CONTINUED FRACTIONS WITH ODD PARTIAL QUOTIENTS

Every Euclidean algorithm is associated with a kind of continued fraction representation of a number. The representation associated with "odd" Euclidean algorithm we will call "odd" continued fraction. We consider the limit distribution function F(x) for sequences of rationals with bounded sum of partial quotients for "odd" continued fractions. In this paper we prove certain properties of the function F(x). Particularly this function is singular and satisfies a number of functional equations. We also show that the value F(x) can be expressed in terms of partial quotients of the "odd" continued fraction representation of a number x.