Series of Error Terms for Rational Approximations of Irrational Numbers

摘要

Let be the -th convergent of a real irrational number , and let . In this paper we investigate various sums of the type , , and . The main subject of the paper is bounds for these sums. In particular, we investigate the behaviour of such sums when is a quadratic surd. The most significant properties of the error sums depend essentially on Fibonacci numbers or on related numbers.