Upper Bounds for Digitwise Generating Functions of Powers of Two: A Problem and a Matrix Representation
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908604509978624 |
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| author | Noda, Hideaki |
| author_facet | Noda, Hideaki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18414 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Upper Bounds for Digitwise Generating Functions of Powers of Two: A Problem and a Matrix Representation Noda, Hideaki Combinatorics Number Theory Probability Primary 11K16, Secondary 11A63, 60F10 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. |
| title | Upper Bounds for Digitwise Generating Functions of Powers of Two: A Problem and a Matrix Representation |
| topic | Combinatorics Number Theory Probability Primary 11K16, Secondary 11A63, 60F10 |
| url | https://arxiv.org/abs/2510.18414 |