Note on the absence of remainders in the Wiener-Ikehara theorem

Debruyne, Gregory; Vindas, Jasson

doi:10.1090/proc/14193

Note on the absence of remainders in the Wiener-Ikehara theorem
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by Gregory Debruyne and Jasson Vindas PDF

Proc. Amer. Math. Soc. 146 (2018), 5097-5103 Request permission

Abstract:

We show that it is impossible to get a better remainder than the classical one in the Wiener-Ikehara theorem even if one assumes analytic continuation of the Mellin transform after subtraction of the pole to a half-plane. We also prove a similar result for the Ingham-Karamata theorem.

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