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Note on the absence of remainders in the Wiener-Ikehara theorem (1801.03491v2)
Published 10 Jan 2018 in math.CA, math.CV, math.FA, and math.NT
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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