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.References
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Additional Information
- Gregory Debruyne
- Affiliation: Department of Mathematics, Ghent University, Krijgslaan 281, B 9000 Gent, Belgium
- MR Author ID: 1185560
- Email: gregory.debruyne@ugent.be
- Jasson Vindas
- Affiliation: Department of Mathematics, Ghent University, Krijgslaan 281, B 9000 Gent, Belgium
- MR Author ID: 795097
- ORCID: 0000-0002-3789-8577
- Email: jasson.vindas@ugent.be
- Received by editor(s): January 10, 2018
- Received by editor(s) in revised form: April 8, 2018, and April 11, 2018
- Published electronically: August 14, 2018
- Additional Notes: The first author gratefully acknowledges support by Ghent University through a BOF Ph.D. grant.
The work of the second author was supported by Ghent University through the BOF grant 01J11615 and by the Research Foundation–Flanders through the FWO grant 1520515N - Communicated by: Stephan Ramon Garcia
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 5097-5103
- MSC (2010): Primary 11M45, 40E05, 44A10
- DOI: https://doi.org/10.1090/proc/14193
- MathSciNet review: 3866849