A note on Arithmetic Diophantine series

TL;DR

This paper explores asymptotic properties of series connected to Diophantine approximation, building on classical work by Hardy, Littlewood, and Davenport, and discusses implications related to the Riemann Hypothesis.

Contribution

It provides new insights into the asymptotic behavior of arithmetic series associated with Diophantine approximation and extends previous analyses involving the Riemann Hypothesis.

Findings

Asymptotic formulas for Diophantine series derived

Connections between series behavior and RH discussed

Extensions of classical results on arithmetic series

Abstract

We consider some asymptotic analysis for series related to the work of Hardy and Littlewood on Diophantine approximation, as well as Davenport. In particular, we expand on ideas from some previous work on arithmetic series and the RH.