论文标题
指数期和O最小性
Exponential periods and o-minimality
论文作者
论文摘要
令$α\ in \ mathbb {c} $为指数期。我们表明，$α$的真实和虚构部分可以在由$ \ mathbb {q} $，真实的指数函数和$ {\ sin} | _ {[0,1]} $中生成的o最小结构中的符号。这是对普通周期的精确表征的一个弱类似物，因为数字的真实和虚构零件是$ \ mathbb {q} $ - 半级别的符号。此外，我们定义了一个天真的指数期的概念，并使用共同体方法将其与现有概念进行比较。这表明时期理论与O最低结构之间的关系。
Let $α\in \mathbb{C}$ be an exponential period. We show that the real and imaginary part of $α$ 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.
