The log moments of smallest denominators

Jens Marklof

doi:10.48550/arXiv.2312.15303

The log moments of smallest denominators

Jens Marklof

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Abstract

This paper studies the logarithmic moments of the smallest denominator of all rationals in a shrinking interval with random center. Convergence follows from the more general results by the author, and the key point of this note is the derivation of explicit formulas for the moments of the limit distribution in dimension one. This answers questions raised by Meiss and Sander in their numerical study of minimal resonance orders for torus maps with random rotation vectors.

Original language	English
Article number	A55
Number of pages	13
Journal	Integers
Volume	24
DOIs	https://doi.org/10.48550/arXiv.2312.15303 https://doi.org/10.5281/zenodo.12167470
Publication status	Published - 19 Jun 2024

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10.48550/arXiv.2312.15303Licence: CC BY
10.5281/zenodo.12167470

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This is the accepted author manuscript (AAM) of the article which has been made Open Access under the University of Bristol's Scholarly Works Policy. The final published version (Version of Record) can be found on the publisher's website. The copyright of any third-party content, such as images, remains with the copyright holder.
Accepted author manuscript, 1.59 MBLicence: CC BY

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abstract = "This paper studies the logarithmic moments of the smallest denominator of all rationals in a shrinking interval with random center. Convergence follows from the more general results by the author, and the key point of this note is the derivation of explicit formulas for the moments of the limit distribution in dimension one. This answers questions raised by Meiss and Sander in their numerical study of minimal resonance orders for torus maps with random rotation vectors.",

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AB - This paper studies the logarithmic moments of the smallest denominator of all rationals in a shrinking interval with random center. Convergence follows from the more general results by the author, and the key point of this note is the derivation of explicit formulas for the moments of the limit distribution in dimension one. This answers questions raised by Meiss and Sander in their numerical study of minimal resonance orders for torus maps with random rotation vectors.

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M3 - Article (Academic Journal)

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The log moments of smallest denominators

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