On the absence of remainders in the Wiener-Ikehara and Ingham-Karamata theorems: A constructive approach
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- by Frederik Broucke, Gregory Debruyne and Jasson Vindas PDF
- Proc. Amer. Math. Soc. 149 (2021), 1053-1060 Request permission
Abstract:
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 theorem under just an additional analytic continuation hypothesis to a half-plane (or even to the whole complex plane).References
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Additional Information
- Frederik Broucke
- Affiliation: Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, 9000 Gent, Belgium
- MR Author ID: 1380112
- ORCID: 0000-0002-5744-4767
- Email: fabrouck.broucke@ugent.be
- Gregory Debruyne
- Affiliation: Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, 9000 Gent, Belgium
- MR Author ID: 1185560
- Email: gregory.debruyne@ugent.be
- Jasson Vindas
- Affiliation: Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, 9000 Gent, Belgium
- MR Author ID: 795097
- ORCID: 0000-0002-3789-8577
- Email: jasson.vindas@ugent.be
- Received by editor(s): January 8, 2020
- Received by editor(s) in revised form: July 29, 2020
- Published electronically: January 22, 2021
- Additional Notes: The first author was supported by the Ghent University BOF-grant 01J04017.
The second author acknowledges support by Postdoctoral Research Fellowships of the Research Foundation–Flanders and the Belgian American Educational Foundation. The latter one allowed him to do part of this research at the University of Illinois at Urbana-Champaign.
The third author was partly supported by Ghent University through the BOF-grant 01J04017 and by the Research Foundation–Flanders through the FWO-grant 1510119N
The third author is the corresponding author. - Communicated by: Javad Mashreghi
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 149 (2021), 1053-1060
- MSC (2020): Primary 11M45, 40E05, 44A10
- DOI: https://doi.org/10.1090/proc/15320
- MathSciNet review: 4211861