Exponential periods and o-minimality
| Autor: | Commelin, Johan, Habegger, Philipp, Huber, Annette |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $\alpha \in \mathbb{C}$ be an exponential period. We show that the real and imaginary part of $\alpha$ are up to signs volumes of sets definable in the o-minimal structure generated by $\mathbb{Q}$, the real exponential function and ${\sin}|_{[0,1]}$. This is a weaker analogue of the precise characterisation of ordinary periods as numbers whose real and imaginary part are up to signs volumes of $\mathbb{Q}$-semi-algebraic sets. Furthermore, we define a notion of naive exponential periods and compare it to the existing notions using cohomological methods. This points to a relation between the theory of periods and o-minimal structures. Comment: 64 pages. The paper is a merger of "Exponential periods and o-minimality I" (v1 of this submission) and "Exponential periods and o-minimality II", previously arXiv:2007.08290 |
| Databáze: | arXiv |
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