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

Institut for Matematiske Fag

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › 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.

Originalsprog	Engelsk
Artikelnummer	125601
Tidsskrift	Expositiones Mathematicae
ISSN	0723-0869
DOI	https://doi.org/10.1016/j.exmath.2024.125601
Status	E-pub ahead of print - 2024

Bibliografisk note

Publisher Copyright:
© 2024 The Author(s)

Adgang til dokumentet

10.1016/j.exmath.2024.125601Licens: CC BY

Citationsformater

@article{b55580e21354426f9c2612511b48376e,

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

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.",

keywords = "Bernstein function, Complete Bernstein function, Pick function, Stieltjes function",

author = "Christian Berg",

note = "Publisher Copyright: {\textcopyright} 2024 The Author(s)",

year = "2024",

doi = "10.1016/j.exmath.2024.125601",

language = "English",

journal = "Expositiones Mathematicae",

issn = "0723-0869",

publisher = "Elsevier GmbH - Urban und Fischer",

}

TY - JOUR

T1 - A complete Bernstein function related to the fractal dimension of Pascal's pyramid modulo a prime

AU - Berg, Christian

PY - 2024

Y1 - 2024

N2 - 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.

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.

KW - Bernstein function

KW - Complete Bernstein function

KW - Pick function

KW - Stieltjes function

UR - http://www.scopus.com/inward/record.url?scp=85200946212&partnerID=8YFLogxK

U2 - 10.1016/j.exmath.2024.125601

DO - 10.1016/j.exmath.2024.125601

M3 - Journal article

AN - SCOPUS:85200946212

JO - Expositiones Mathematicae

JF - Expositiones Mathematicae

SN - 0723-0869

M1 - 125601

ER -