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arXiv · 2510.18414

Upper Bounds for Digitwise Generating Functions of Powers of Two: A Problem and a Matrix Representation

Hideaki Noda
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Abstract

This short note studies the asymptotic behavior of a generating function associated with the decimal expansion of \(2^n\). Our aims are twofold: (i) to present a problem on the best possible upper bound for this behavior, and (ii) to introduce a matrix representation that is useful for its analysis. The representation corresponds to a finite-state transfer operator; analytic and dynamical aspects are not pursued here.

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Hideaki Noda. 2025-10-21. Upper Bounds for Digitwise Generating Functions of Powers of Two: A Problem and a Matrix Representation. https://arxiv.org/abs/2510.18414

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