Large and moderate deviation principles for Engel continued fractions

TL;DR

This paper establishes large and moderate deviation principles for Engel continued fractions, a novel class of continued fractions characterized by non-decreasing partial quotients, expanding understanding in number theory.

Contribution

It introduces the first large and moderate deviation principles specifically for Engel continued fractions, a new type of continued fraction expansion.

Findings

Proved large deviation principles for Engel continued fractions.

Established moderate deviation principles for this new class.

Enhanced theoretical understanding of number theoretic properties.

Abstract

Large and moderate deviation principles are proved for Engel continued fractions, a new type of continued fraction expansion with non-decreasing partial quotients in number theory.