Geodesic
Multisummability for generalized power series
Canadian journal of mathematics, Tome 76 (2024) no. 2, pp. 458-494

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DOI

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 $\mathbb {R}_{\text {an}^*}$ 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 $(1,\infty )$.
DOI : 10.4153/S0008414X23000111
Mots-clés : Gamma function, zeta function, multisummability, quasianalyticity, o-minimality 
Rolin, Jean-Philippe; Servi, Tamara; Speissegger, Patrick. Multisummability for generalized power series. Canadian journal of mathematics, Tome 76 (2024) no. 2, pp. 458-494. doi: 10.4153/S0008414X23000111
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     title = {Multisummability for generalized power series},
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     year = {2024},
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