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

Christian Berg

doi:10.1016/j.exmath.2024.125601

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

Christian Berg

Department of Mathematical Sciences

Research output: Contribution to journal › Journal article › Research › peer-review

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≤r≤1 and a Stieltjes function for 1≤r. This answers a conjecture of David Bradley that f_r is a Bernstein function when 0≤r≤1.

Original language	English
Article number	125601
Journal	Expositiones Mathematicae
ISSN	0723-0869
DOIs	https://doi.org/10.1016/j.exmath.2024.125601
Publication status	E-pub ahead of print - 2024

Bibliographical note

Publisher Copyright:
© 2024 The Author(s)

Keywords

Bernstein function
Complete Bernstein function
Pick function
Stieltjes function

Access to Document

10.1016/j.exmath.2024.125601Licence: CC BY

Cite this

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abstract = "Let fr(x)=log(1+rx)/log(1+x) for x>0. We prove that fr is a complete Bernstein function for 0≤r≤1 and a Stieltjes function for 1≤r. This answers a conjecture of David Bradley that fr is a Bernstein function when 0≤r≤1.",

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AB - Let fr(x)=log(1+rx)/log(1+x) for x>0. We prove that fr is a complete Bernstein function for 0≤r≤1 and a Stieltjes function for 1≤r. This answers a conjecture of David Bradley that fr is a Bernstein function when 0≤r≤1.

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KW - Complete Bernstein function

KW - Pick function

KW - Stieltjes function

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