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arXiv · 2402.08378

A complete Bernstein function related to the fractal dimension of Pascal's pyramid modulo a prime

Christian Berg
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Abstract

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 $0\le r\le 1$.

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Christian Berg. 2024-02-13. A complete Bernstein function related to the fractal dimension of Pascal's pyramid modulo a prime. https://arxiv.org/abs/2402.08378

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