## S Kanemitsu ; T Kuzumaki ; Y Tanigawa - On the Wintner-Ingham-Segal summability method

hrj:5104 - Hardy-Ramanujan Journal, January 23, 2019 - https://doi.org/10.46298/hrj.2019.5104
On the Wintner-Ingham-Segal summability method

Authors: S Kanemitsu ; T Kuzumaki ; Y Tanigawa

The aim of this note is to establish a subclass of $\mathcal{F}$ considered by Segal if functions for which the Ingham-Wintner summability implies $\mathcal{F}$-summability as wide as possible. The subclass is subject to the estimate for the error term of the prime number theorem. We shall make good use of Stieltjes integration which elucidates previous results obtained by Segal.

Published on: January 23, 2019
Submitted on: January 23, 2019
Keywords: (Ingham) summability,zero-free region,Stieltjes integral,weak Riemann hypothesis 2010 Mathematics Subject Classification 40D99,11M99, [ MATH ] Mathematics [math], [ MATH.MATH-NT ] Mathematics [math]/Number Theory [math.NT]