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Journal Articles Hardy-Ramanujan Journal Year : 2019

On the Wintner-Ingham-Segal summability method

Abstract

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.
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Dates and versions

hal-01985935 , version 1 (18-01-2019)

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S Kanemitsu, T Kuzumaki, Y Tanigawa. On the Wintner-Ingham-Segal summability method. Hardy-Ramanujan Journal, 2019, Atelier Digit_Hum, pp.40 - 47. ⟨10.46298/hrj.2019.5104⟩. ⟨hal-01985935⟩
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