A Sankaranarayanan ; Saurabh Kumar Singh - On the Riesz means of nϕ(n)

hrj:179 - Hardy-Ramanujan Journal, January 1, 2013, Volume 36 - 2013 - https://doi.org/10.46298/hrj.2013.179
On the Riesz means of nϕ(n)Article

Authors: A Sankaranarayanan 1; Saurabh Kumar Singh 1

Let ϕ(n) denote the Euler-totient function. We study the error term of the general k-th Riesz mean of the arithmetical function nϕ(n) for any positive integer k1, namely the error term Ek(x) where1k!nxnϕ(n)(1nx)k=Mk(x)+Ek(x).

The upper bound for |Ek(x)| established here thus improves the earlier known upper bound when k=1.


Volume: Volume 36 - 2013
Published on: January 1, 2013
Imported on: March 3, 2015
Keywords: Euler-totient function,Generating functions,Riemann zeta-function,mean-value theorems,[MATH]Mathematics [math]

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