On the Riesz means of n/ϕ(n) - III

Ayyadurai Sankaranarayanan, and Saurabh Kumar Singh. "On the Riesz means of n/ϕ(n) - III." Acta Arithmetica 170.3 (2015): 275-286. <http://eudml.org/doc/279380>.

@article{AyyaduraiSankaranarayanan2015,
abstract = {Let ϕ(n) denote the Euler totient function. We study the error term of the general kth Riesz mean of the arithmetical function n/ϕ(n) for any positive integer k ≥ 1, namely the error term $E_k(x)$ where $1/k! ∑_\{n≤x\} n/ϕ(n) (1 - n/x)^\{k\} = M_k(x) + E_k(x)$. For instance, the upper bound for |Ek(x)| established here improves the earlier known upper bounds for all integers k satisfying $k ≫ (log x)^\{1+ϵ\}$.},
author = {Ayyadurai Sankaranarayanan, Saurabh Kumar Singh},
journal = {Acta Arithmetica},
keywords = {Euler totient function; generating functions; Riemann zeta-function; mean-value theorems},
language = {eng},
number = {3},
pages = {275-286},
title = {On the Riesz means of n/ϕ(n) - III},
url = {http://eudml.org/doc/279380},
volume = {170},
year = {2015},
}

TY - JOUR
AU - Ayyadurai Sankaranarayanan
AU - Saurabh Kumar Singh
TI - On the Riesz means of n/ϕ(n) - III
JO - Acta Arithmetica
PY - 2015
VL - 170
IS - 3
SP - 275
EP - 286
AB - Let ϕ(n) denote the Euler totient function. We study the error term of the general kth Riesz mean of the arithmetical function n/ϕ(n) for any positive integer k ≥ 1, namely the error term $E_k(x)$ where $1/k! ∑_{n≤x} n/ϕ(n) (1 - n/x)^{k} = M_k(x) + E_k(x)$. For instance, the upper bound for |Ek(x)| established here improves the earlier known upper bounds for all integers k satisfying $k ≫ (log x)^{1+ϵ}$.
LA - eng
KW - Euler totient function; generating functions; Riemann zeta-function; mean-value theorems
UR - http://eudml.org/doc/279380
ER -