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On the absence of remainders in the Wiener-Ikehara and Ingham-Karamata theorems: a constructive approach (2001.01635v2)
Published 6 Jan 2020 in math.CA, math.CV, and math.NT
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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