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arXiv · 2001.01635

On the absence of remainders in the Wiener-Ikehara and Ingham-Karamata theorems: a constructive approach

Frederik Broucke·Gregory Debruyne·Jasson Vindas
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Abstract

We construct explicit counterexamples that show that it is impossible to get any remainder, other than the classical ones, in the Wiener-Ikehara theorem and the Ingham-Karamata theorem under just an additional analytic continuation hypothesis to a half-plane (or even to the whole complex plane).

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Frederik Broucke, Gregory Debruyne, Jasson Vindas. 2020-01-06. On the absence of remainders in the Wiener-Ikehara and Ingham-Karamata theorems: a constructive approach. https://doi.org/10.1090/proc/15320

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