Prolongations of t-motives and algebraic independence of periods
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2017
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| _version_ | 1866911459874701312 |
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| author | Maurischat, Andreas |
| author_facet | Maurischat, Andreas |
| contents | In this article we show that the coordinates of a period lattice generator of the $n$-th tensor power of the Carlitz module are algebraically independent, if $n$ is prime to the characteristic. The main part of the paper, however, is devoted to a general construction for $t$-motives which we call prolongation, and which gives the necessary background for our proof of the algebraic independence. Another ingredient is a theorem which shows hypertranscendence for the Anderson-Thakur function $ω(t)$, i.e. that $ω(t)$ and all its hyperderivatives with respect to $t$ are algebraically independent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1710_08252 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Prolongations of t-motives and algebraic independence of periods Maurischat, Andreas Number Theory 11J93 (Primary), 11G09, 13N99 (Secondary) In this article we show that the coordinates of a period lattice generator of the $n$-th tensor power of the Carlitz module are algebraically independent, if $n$ is prime to the characteristic. The main part of the paper, however, is devoted to a general construction for $t$-motives which we call prolongation, and which gives the necessary background for our proof of the algebraic independence. Another ingredient is a theorem which shows hypertranscendence for the Anderson-Thakur function $ω(t)$, i.e. that $ω(t)$ and all its hyperderivatives with respect to $t$ are algebraically independent. |
| title | Prolongations of t-motives and algebraic independence of periods |
| topic | Number Theory 11J93 (Primary), 11G09, 13N99 (Secondary) |
| url | https://arxiv.org/abs/1710.08252 |