The values of the periodic zeta-function at the nontrivial zeros of Riemann's zeta-function
Please always quote using this URN: urn:nbn:de:bvb:20-opus-252261
- In this paper, we prove an asymptotic formula for the sum of the values of the periodic zeta-function at the nontrivial zeros of the Riemann zeta-function (up to some height) which are symmetrical on the real line and the critical line. This is an extension of the previous results due to Garunkštis, Kalpokas, and, more recently, Sowa. Whereas Sowa's approach was assuming the yet unproved Riemann hypothesis, our result holds unconditionally.
| Author: | Janyarak Tongsomporn, Saeree Wananiyakul, Jörn Steuding |
|---|---|
| URN: | urn:nbn:de:bvb:20-opus-252261 |
| Document Type: | Journal article |
| Faculties: | Fakultät für Mathematik und Informatik / Institut für Mathematik |
| Language: | English |
| Parent Title (English): | Symmetry |
| ISSN: | 2073-8994 |
| Year of Completion: | 2021 |
| Volume: | 13 |
| Issue: | 12 |
| Article Number: | 2410 |
| Source: | Symmetry (2021) 13:12, 2410. https://doi.org/10.3390/sym13122410 |
| DOI: | https://doi.org/10.3390/sym13122410 |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Tag: | Riemann hypothesis; zeta-functions |
| Release Date: | 2022/12/14 |
| Date of first Publication: | 2021/12/13 |
| Licence (German): |  CC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International |