What question did this study set out to answer?

The aim is to establish a relation for error terms in asymptotic formulas for the associated Euler totient function, akin to a previous result by H.L. Montgomery.

April 10, 2026Open Access

A Relation for the Remainder Terms in an Asymptotic Formula for the Associated Euler Totient

Key Points

The aim is to establish a relation for error terms in asymptotic formulas for the associated Euler totient function, akin to a previous result by H.L. Montgomery.
Examined the associated Euler totient function defined by J. Kaczorowski.
Relied on previous findings from H.L. Montgomery regarding error terms in similar functions.
Developed a mathematical proof for a specific case of the associated Euler totient function.
Confirmed a relation for error terms that parallels Montgomery's findings.
Established the asymptotic behavior of the associated Euler totient function for broader applications.

Abstract

For any positive integer n, H.L.Montgomery proved a relation for error terms in asymptotic formulas for the Euler totient function (n).J.Kaczorowski defined the associated Euler totient function which generalizes (n) and obtained an asymptotic formula for it.In this paper, we prove a relation for error terms similar to H.L.Montgomery's result for a certain special case of the associated Euler totient function.

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