Attainable measures for certain types of p-adic Duffin-Schaeffer sets

Mathias Løkkegaard Laursen

doi:10.7146/math.scand.a-139832

Attainable measures for certain types of p-adic Duffin-Schaeffer sets

Department of Mathematics

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Abstract

This paper settles recent conjectures concerning the p-adic Haar measure applied to a family of sets defined in terms of Diophantine approximation. This is done by determining the spectrum of measure values for each family and seeing that this contradicts the corresponding conjectures.

Original language	English
Article number	3
Journal	Mathematica Scandinavica
Volume	129
Issue	3
Pages (from-to)	452-480
Number of pages	29
ISSN	0025-5521
DOIs	https://doi.org/10.7146/math.scand.a-139832
Publication status	Published - Oct 2023

Keywords

METRIC THEORY
p-adic analogues

Access to Document

10.7146/math.scand.a-139832

https://arxiv.org/abs/2212.03619

1 Journal article

The p-adic Duffin–Schaeffer Conjecture
Kristensen, S. & Laursen, M. L., Mar 2023, In: Functiones et Approximatio Commentarii Mathematici. 68, 1, p. 113-126 14 p.
Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

1 Citation (Scopus)

Cite this

@article{6404bd80f119457086263df3016fed22,

title = "Attainable measures for certain types of p-adic Duffin-Schaeffer sets",

abstract = "This paper settles recent conjectures concerning the p-adic Haar measure applied to a family of sets defined in terms of Diophantine approximation. This is done by determining the spectrum of measure values for each family and seeing that this contradicts the corresponding conjectures.",

keywords = "METRIC THEORY, p-adic analogues",

author = "Laursen, {Mathias L{\o}kkegaard}",

year = "2023",

month = oct,

doi = "10.7146/math.scand.a-139832",

language = "English",

volume = "129",

pages = "452--480",

journal = "Mathematica Scandinavica",

issn = "0025-5521",

publisher = "Mathematica Scandinavica",

number = "3",

}

TY - JOUR

T1 - Attainable measures for certain types of p-adic Duffin-Schaeffer sets

AU - Laursen, Mathias Løkkegaard

PY - 2023/10

Y1 - 2023/10

N2 - This paper settles recent conjectures concerning the p-adic Haar measure applied to a family of sets defined in terms of Diophantine approximation. This is done by determining the spectrum of measure values for each family and seeing that this contradicts the corresponding conjectures.

AB - This paper settles recent conjectures concerning the p-adic Haar measure applied to a family of sets defined in terms of Diophantine approximation. This is done by determining the spectrum of measure values for each family and seeing that this contradicts the corresponding conjectures.

KW - METRIC THEORY

KW - p-adic analogues

U2 - 10.7146/math.scand.a-139832

DO - 10.7146/math.scand.a-139832

M3 - Journal article

SN - 0025-5521

VL - 129

SP - 452

EP - 480

JO - Mathematica Scandinavica

JF - Mathematica Scandinavica

IS - 3

M1 - 3

ER -

Attainable measures for certain types of p-adic Duffin-Schaeffer sets

Abstract

Keywords

Access to Document

Fingerprint

Research output

The p-adic Duffin–Schaeffer Conjecture

Cite this