论文标题
通用功率系列的多重性能
Multisummability for generalized power series
论文作者
论文摘要
我们在积极的真实方向上开发了具有自然支持的广义功率序列的多功能性，并且通过这些系列的所有多量，我们证明了真实领域扩展的o最小程度。这种结果结构都扩展了$ \ mathbb {r} _ {\ Mathcal {g}} $和$ \ Mathbb {r} _ {\ Mathrm {\ Mathrm {an}^*} $的$ \ MathBb {r} _ {特别是，其通过指数函数的扩展将gamma函数定义为$（0，\ infty）$，又定义了$（1，\ infty）$的Zeta函数。
We develop multisummability, in the positive real direction, for generalized power series with natural support, and we prove o-minimality of the expansion of the real field by all multisums of these series. This resulting structure expands both $\mathbb{R}_{\mathcal{G}}$ and the reduct of $\mathbb{R}_{\mathrm{an}^*}$ generated by all convergent generalized power series with natural support; in particular, its expansion by the exponential function defines both the Gamma function on $(0,\infty)$ and the Zeta function on $(1,\infty)$.
