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

Frederik Broucke, Gregory Debruyne, Jasson Vindas

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 the…