Year: 2024
Type: article
Abstract: In 1930, G. H. Hardy and J. E. Littlewood derived results concerning rates of divergence of certain series involving cosecants. In more recent terminology, one of their results can be interpreted in terms of the behaviour of orbits in a dynamical system that is a rotation on the unit circle. Now, the expansion of numbers in the unit interval \([0,1)\) to the base \(2\) can be associated with a different dynamical system − the binary system. This article considers orbit behaviour in the binary system that corresponds, in part, to the behaviour that was observed by Hardy and Littlewood in a different context. A number in \([0,1)\) is called a binary rational if it is of the form \(k/2^n\) for some \(0\leqslant k
Source: Real Analysis Exchange
Author: Rodney Nillsen
Institution: University of Wollongong
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403461002