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September 2021 On a generalization of the Euler totient function
Zhai Wenguang
Funct. Approx. Comment. Math. 65(1): 119-139 (September 2021). DOI: 10.7169/facm/1917

Abstract

In a recent paper, J. Kaczorowski defined the generalized Euler totient function $\varphi(n, F)$ corresponding to a polynomial Euler product $F$. Let $E(x, F)$ denote the error term in the asymptotic formula of the summatory function of $\varphi(n, F).$ J.~Kaczorowski proved that the mean square of $E(x, F)$ has an asymptotic formula if $F$ satisfies GRH. In this paper we shall prove a sharper asymptotic formula under GRH.

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Zhai Wenguang. "On a generalization of the Euler totient function." Funct. Approx. Comment. Math. 65 (1) 119 - 139, September 2021. https://doi.org/10.7169/facm/1917

Information

Published: September 2021
First available in Project Euclid: 22 January 2021

Digital Object Identifier: 10.7169/facm/1917

Subjects:
Primary: 11M41, 11N37

Rights: Copyright © 2021 Adam Mickiewicz University

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Vol.65 • No. 1 • September 2021
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