论文标题
指数期和O最小性II
Exponential periods and o-minimality II
论文作者
论文摘要
本文是作者与菲利普·哈贝格（Philipp Habegger）一起写作的“指数时期和O最小程度I”的续集。我们完成了指数期不同定义之间的比较，并表明它们都导致了相同的概念。在第一篇论文中，我们表明天真的指数期是绝对收敛的指数期。我们还表明，幼稚的指数周期可达到由$ \ mathbb {q} $，真实的指数函数和$ {\ sin} | _ {[0,1]} $生成的O-Minimal结构中可定义集的符号。 在本文中，我们将这些定义与指数NORI动机的共同指数期和时期进行了比较。特别是，幼稚的指数周期与指数NORI动机的时期相同，这证明对幼稚的指数周期的定义是挑出正确的一组正确的复数集，称为指数期。
This paper is a sequel to "Exponential periods and o-minimality I" that the authors wrote together with Philipp Habegger. We complete the comparison between different definitions of exponential periods, and show that they all lead to the same notion. In the first paper, we show that naive exponential periods are absolutely convergent exponential periods. We also show that naive exponential periods are up to signs volumes of definable sets in the o-minimal structure generated by $\mathbb{Q}$, the real exponential function and ${\sin}|_{[0,1]}$. In this paper, we compare these definitions with cohomological exponential periods and periods of exponential Nori motives. In particular, naive exponential periods are the same as periods of exponential Nori motives, which justifies that the definition of naive exponential periods singles out the correct set of complex numbers to be called exponential periods.
