Multisummability for generalized power series - Archive ouverte HAL
Article Dans Une Revue Canadian Journal of Mathematics Année : 2023

Multisummability for generalized power series

Résumé

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 $(1,\infty)$.
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hal-03836697 , version 1 (02-02-2024)

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Jean-Philippe Rolin, Tamara Servi, Patrick Speissegger. Multisummability for generalized power series. Canadian Journal of Mathematics, 2023, pp.1-37. ⟨10.4153/S0008414X23000111⟩. ⟨hal-03836697⟩
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