eng
episciences.org
Hardy-Ramanujan Journal
2804-7370
2019-01-23
10.46298/hrj.2019.5104
5104
journal article
On the Wintner-Ingham-Segal summability method
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.
https://hrj.episciences.org/5104/pdf
(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]