Multisummability for generalized power series

Abstract

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 ${\mathbb{R}}_{{\mathrm{an}}^{\ast }}$ 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 $(1,\infty )$.

34 pages