Quantitative generalizations of Niederreiter's result concerning continuants

TL;DR

This paper extends Niederreiter's results related to Zaremba's conjecture, which concerns the existence of rational numbers with bounded partial quotients, providing a broader mathematical framework.

Contribution

It introduces a generalization of Niederreiter's theorem, advancing the understanding of rational approximations with bounded partial quotients.

Findings

Generalized Niederreiter's result on continuants

Enhanced understanding of Zaremba's conjecture

Potential implications for number theory

Abstract

We give certain generalization of Niederreiter's result concerning famous Zaremba's conjecture on existence of rational numbers with bounded partial quotients.