A NEW PROOF OF THE SINGULAR CONTINUITY OF THE MINKOWSKI $?$-FUNCTION

Abstract We give a new proof of the singular continuity of Minkowski’s $?$ -function. Our proof follows by showing that the maximal Lyapunov exponent of a specific pair of $3\times 3$ nonnegative integer matrices related to Stern’s diatomic sequence is strictly greater than $\log 2$ .

Authors

Michael James Coons (ORCID: https://orcid.org/0000-0001-9093-0815)
D. Wood
ARI PINCUS KAZMAR
SAMUEL COYLE (ORCID: https://orcid.org/0009-0009-1491-187X)
ADAM STOUT

Institutions

California State University System (US)
University of Minnesota (US)
University of Minnesota System (US)
California State University, Chico (US)
Macalester College (US)

Publication Details

Journal: Bulletin of the Australian Mathematical Society
Published: 2025-12-04
DOI: https://doi.org/10.1017/s0004972725100701
Primary Topic: Approximation Theory and Sequence Spaces
Type: article
Field-Weighted Citation Impact: 0.00

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article

A NEW PROOF OF THE SINGULAR CONTINUITY OF THE MINKOWSKI $?$-FUNCTION

Michael James Coons, D. Wood, ARI PINCUS KAZMAR, SAMUEL COYLE et al.

Dec 4, 2025

Bulletin of the Australian Mathematical Society

Approximation Theory and Sequence Spaces

article

A NEW PROOF OF THE SINGULAR CONTINUITY OF THE MINKOWSKI $?$-FUNCTION

Michael James Coons, D. Wood, ARI PINCUS KAZMAR, SAMUEL COYLE, ADAM STOUT

December 4, 2025article en

Abstract

Abstract We give a new proof of the singular continuity of Minkowski’s $?$ -function. Our proof follows by showing that the maximal Lyapunov exponent of a specific pair of $3\times 3$ nonnegative integer matrices related to Stern’s diatomic sequence is strictly greater than $\log 2$ .

Bulletin of the Australian Mathematical Society

California State University System (US), University of Minnesota (US), University of Minnesota System (US), California State University, Chico (US), Macalester College (US)

Openalex Percentile: Top 65%

Approximation Theory and Sequence Spaces

DOI Open Access PDF OpenAlex

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A NEW PROOF OF THE SINGULAR CONTINUITY OF THE MINKOWSKI $?$-FUNCTION — Michael James Coons, D. Wood, et al. · Bulletin of the Australian Mathematical Society (2025) | TGRS Research Map | TGRS