Large and moderate deviation principles for Engel continued fractions

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.

arXiv comment24 pages

References in corpus (5)

• The large deviation approach to statistical mechanics
• On large deviations of additive functions
• A note on Rényi's "record" problem and Engel's series
• Limit Theorems for Empirical Density of Greatest Common Divisors
• Moderate deviations and laws of the iterated logarithm for the local times of additive Lévy processes and additive random walks

Cited by in corpus (1)

• A note on Rényi's "record" problem and Engel's series