2023/02/27 by Jean-Philippe Rolin, Tamara Servi, Patrick Speissegger · 1 citation
Mathematics · #Advanced Topology and Set Theory #Rings, Modules, and Algebras #Functional Equations Stability Results
paper · pdf · doi:10.4153/s0008414x23000111
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_\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,∞ ) and the zeta function on (1,∞ ) .