Mahler series with multiplicative coefficient sequences
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912980849917952 |
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| author | Bell, Jason Smertnig, Daniel |
| author_facet | Bell, Jason Smertnig, Daniel |
| contents | We prove that every Mahler series, over a field of characteristic $0$, with multiplicative coefficients is regular in the sense of Allouche and Shallit. We also obtain an explicit characterization of such series. This yields a joint extension of the characterization of rational series with multiplicative coefficients (by Bézivin and Bell--Bruin--Coons) and of multiplicative automatic sequences (by Konieczny--Lemańczyk--Müllner). Both of these results are used in our characterization, so we do not obtain new proofs of these special cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23456 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mahler series with multiplicative coefficient sequences Bell, Jason Smertnig, Daniel Number Theory Primary 11B85, Secondary 11N64, 39A06 We prove that every Mahler series, over a field of characteristic $0$, with multiplicative coefficients is regular in the sense of Allouche and Shallit. We also obtain an explicit characterization of such series. This yields a joint extension of the characterization of rational series with multiplicative coefficients (by Bézivin and Bell--Bruin--Coons) and of multiplicative automatic sequences (by Konieczny--Lemańczyk--Müllner). Both of these results are used in our characterization, so we do not obtain new proofs of these special cases. |
| title | Mahler series with multiplicative coefficient sequences |
| topic | Number Theory Primary 11B85, Secondary 11N64, 39A06 |
| url | https://arxiv.org/abs/2603.23456 |