On the Riesz means of n/ϕ(n) - III

• Autorzy: Ayyadurai Sankaranarayanan , Saurabh Kumar Singh
• Języki publikacji: EN

Abstrakty

EN

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 |E_k(x)| established here improves the earlier known upper bounds for all integers k satisfying $k ≫ (log x)^{1+ϵ}$.

Kategorie tematyczne

• 11N37: Asymptotic results on arithmetic functions
• 11A25: Arithmetic functions; related numbers; inversion formulas

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 170
• Numer: 3
• Strony: 275-286

Daty

wydano

2015

Twórcy

autor

Ayyadurai Sankaranarayanan

• School of Mathematics, Tata Institute of Fundamental Research (TIFR), Homi Bhabha Road, Mumbai 400 005, India

autor

Saurabh Kumar Singh

• School of Mathematics, Tata Institute of Fundamental Research (TIFR), Homi Bhabha Road, Mumbai 400 005, India

Identyfikatory

DOI

10.4064/aa170-3-4