A complete Bernstein function related to the fractal dimension of Pascal's pyramid modulo a prime
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909465973882880 |
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| author | Berg, Christian |
| author_facet | Berg, Christian |
| contents | Let $f_r(x)=\log(1+rx)/\log(1+x)$ for $x>0$. We prove that $f_r$ is a complete Bernstein function for $0\le r\le 1$ and a Stieltjes function for $1\le r$. This answers a conjecture of David Bradley that $f_r$ is a Bernstein function when $0\le r\le 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08378 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A complete Bernstein function related to the fractal dimension of Pascal's pyramid modulo a prime Berg, Christian Classical Analysis and ODEs Number Theory 30E20, 26A48 Let $f_r(x)=\log(1+rx)/\log(1+x)$ for $x>0$. We prove that $f_r$ is a complete Bernstein function for $0\le r\le 1$ and a Stieltjes function for $1\le r$. This answers a conjecture of David Bradley that $f_r$ is a Bernstein function when $0\le r\le 1$. |
| title | A complete Bernstein function related to the fractal dimension of Pascal's pyramid modulo a prime |
| topic | Classical Analysis and ODEs Number Theory 30E20, 26A48 |
| url | https://arxiv.org/abs/2402.08378 |