On sums involving powers of harmonic numbers
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909675612536832 |
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| author | Tin, Lo Ho |
| author_facet | Tin, Lo Ho |
| contents | In this paper, we study a Dirichlet series generated by powers of harmonic numbers. As an application of these functions, we derive certain series involving harmonic numbers. We also study the analytic properties of these Dirichlet series such as values negative integers and behavior at poles. In particular, objects similar to the Stieltjes constants are discussed. Asymptotics of the sums involving harmonic numbers are also studied. From these results I showed a connection between its analytic properties and a possible route to showing the irrationality of the Euler-Mascheroni constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03058 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On sums involving powers of harmonic numbers Tin, Lo Ho Number Theory 11M41 (Primary) 30B40, 30B50 (Secondary) In this paper, we study a Dirichlet series generated by powers of harmonic numbers. As an application of these functions, we derive certain series involving harmonic numbers. We also study the analytic properties of these Dirichlet series such as values negative integers and behavior at poles. In particular, objects similar to the Stieltjes constants are discussed. Asymptotics of the sums involving harmonic numbers are also studied. From these results I showed a connection between its analytic properties and a possible route to showing the irrationality of the Euler-Mascheroni constant. |
| title | On sums involving powers of harmonic numbers |
| topic | Number Theory 11M41 (Primary) 30B40, 30B50 (Secondary) |
| url | https://arxiv.org/abs/2507.03058 |