Sur l'asymptotique des sommes de Kempner pour de grandes bases
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911880627355648 |
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| author | Burnol, Jean-François |
| author_facet | Burnol, Jean-François |
| contents | Let $K$ be the sum of the reciprocals of the integers with no occurrence of the digit $b-1$ in base $b$. We show $K = b\log(b) - A/b - B/b^2-C/b^3+O(1/b^4)$ with $A=ζ(2)/2$, $B = (3ζ(2)+ζ(3))/3$ and $C = (2ζ(2)+4ζ(3)+ζ(4))/4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01957 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sur l'asymptotique des sommes de Kempner pour de grandes bases Burnol, Jean-François Number Theory Classical Analysis and ODEs 11Y60, 11M06 (Primary) 11A63, 11B37, 30C10, 41A60, 44A60 (Secondary) Let $K$ be the sum of the reciprocals of the integers with no occurrence of the digit $b-1$ in base $b$. We show $K = b\log(b) - A/b - B/b^2-C/b^3+O(1/b^4)$ with $A=ζ(2)/2$, $B = (3ζ(2)+ζ(3))/3$ and $C = (2ζ(2)+4ζ(3)+ζ(4))/4$. |
| title | Sur l'asymptotique des sommes de Kempner pour de grandes bases |
| topic | Number Theory Classical Analysis and ODEs 11Y60, 11M06 (Primary) 11A63, 11B37, 30C10, 41A60, 44A60 (Secondary) |
| url | https://arxiv.org/abs/2403.01957 |