Asymptotic evaluation of Euler-phi sums of various residue classes

TL;DR

This paper provides asymptotic formulas for sums of Euler's phi-function over different residue classes, offering insights into their long-term behavior and distribution.

Contribution

It introduces new asymptotic formulas for Euler-phi sums across various residue classes, expanding understanding of their asymptotic properties.

Findings

Derived asymptotic formulas for Euler-phi sums in different residue classes

Enhanced understanding of the distribution of Euler's phi-function

Provided mathematical tools for further number theory research

Abstract

This note contains some asymptotic formulas for the sums of various residue classes of Euler's phi-function.