Mahler's method and Carlitz logarithm
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918399826722816 |
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| author | Estienne, Guillaume |
| author_facet | Estienne, Guillaume |
| contents | In 2007, Papanikolas established that if Carlitz logarithms of algebraic functions are linearly independent over the rational function field, then they are algebraically independent. The purpose of the present paper is to provide a new proof of this theorem using Mahler s method instead of the theory of t-motives. We revisit and extend the approach developed by Denis, which enabled him in 2006 to prove this result in the particular case of the logarithm of elements in Fq(theta) via a Mahler system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18832 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mahler's method and Carlitz logarithm Estienne, Guillaume Number Theory In 2007, Papanikolas established that if Carlitz logarithms of algebraic functions are linearly independent over the rational function field, then they are algebraically independent. The purpose of the present paper is to provide a new proof of this theorem using Mahler s method instead of the theory of t-motives. We revisit and extend the approach developed by Denis, which enabled him in 2006 to prove this result in the particular case of the logarithm of elements in Fq(theta) via a Mahler system. |
| title | Mahler's method and Carlitz logarithm |
| topic | Number Theory |
| url | https://arxiv.org/abs/2603.18832 |