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

1 Citationer (Scopus)

17 Downloads (Pure)

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
Vol/bind	44
Udgave nummer	1
Antal sider	11
ISSN	0723-0869
DOI	https://doi.org/10.1016/j.exmath.2024.125601
Status	Udgivet - 2026

Bibliografisk note

Publisher Copyright:
© 2024 The Author(s)

Adgang til dokumentet

10.1016/j.exmath.2024.125601Licens: CC BY

Full textForlagets udgivne version, 338 KBLicens: CC BY

Biblioteksadgang?

Tjek tilgængelighed hos det Kgl. Bibliotek

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 = "2026",

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

language = "English",

volume = "44",

journal = "Expositiones Mathematicae",

issn = "0723-0869",

publisher = "Elsevier GmbH - Urban und Fischer",

number = "1",

}

TY - JOUR

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

AU - Berg, Christian

PY - 2026

Y1 - 2026

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

U2 - 10.1016/j.exmath.2024.125601

DO - 10.1016/j.exmath.2024.125601

M3 - Journal article

AN - SCOPUS:85200946212

SN - 0723-0869

VL - 44

JO - Expositiones Mathematicae

JF - Expositiones Mathematicae

IS - 1

M1 - 125601

ER -