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September 29, 2025Open Access

A relation to a remainder terms in an asymptotic formula for the associated Euler totient function

Key Points

The paper establishes a link between error terms and asymptotic formulas for the Euler totient function, indicating significant findings.
Key evidence shows a correlation between error terms and known results from Montgomery's work on asymptotic analysis.
The analysis focuses on a special case of the associated Euler totient function, contributing to its theoretical understanding.
Implications of these findings may enhance future research on error terms and related asymptotic properties in number theory.

Abstract

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

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Hideto Iwata (Sun,) studied this question.

www.synapsesocial.com/papers/68da58e0c1728099cfd11901 — DOI: https://doi.org/10.48550/arxiv.2505.19344

A relation to a remainder terms in an asymptotic formula for the associated Euler totient function

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