Newman's Tauberian theorem, the Riemann-Lebesgue Lemma, and abstract analytic number theory
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913065532915712 |
|---|---|
| author | Schlage-Puchta, Jan-Christoph Schwerdt, Christoph |
| author_facet | Schlage-Puchta, Jan-Christoph Schwerdt, Christoph |
| contents | We give a generalized and effective version of Bekehermes' improvement of Newman's Tauberian theorem. To do so we prove an effective version of the Riemann-Lebesgue Lemma for functions of bounded $p$-variation. We apply our Tauberian theorem to abstract analytic semigroups and prove a version of the prime number theorem as well as an estimate for Mertens' function with explicit error term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24505 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Newman's Tauberian theorem, the Riemann-Lebesgue Lemma, and abstract analytic number theory Schlage-Puchta, Jan-Christoph Schwerdt, Christoph Complex Variables Number Theory 40E05, 11M45, 11N80 We give a generalized and effective version of Bekehermes' improvement of Newman's Tauberian theorem. To do so we prove an effective version of the Riemann-Lebesgue Lemma for functions of bounded $p$-variation. We apply our Tauberian theorem to abstract analytic semigroups and prove a version of the prime number theorem as well as an estimate for Mertens' function with explicit error term. |
| title | Newman's Tauberian theorem, the Riemann-Lebesgue Lemma, and abstract analytic number theory |
| topic | Complex Variables Number Theory 40E05, 11M45, 11N80 |
| url | https://arxiv.org/abs/2604.24505 |