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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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Submitted on : Friday, January 18, 2019 - 1:53:22 PM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM

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

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