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arXiv · 1801.03491

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

Gregory Debruyne·Jasson Vindas
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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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Gregory Debruyne, Jasson Vindas. 2018-01-10. Note on the absence of remainders in the Wiener-Ikehara theorem. https://doi.org/10.1090/proc/14193

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