Logic Seminar

Patrick Speissegger, McMaster University

"The real Gamma and Zeta functions are jointly o-minimal"

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 (i) the expansion of the real field by all multisummable (in the positive real direction) power series, and (ii) the reduct of Ran∗ 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, ∞).  (Joint work with Jean-Philippe Rolin and Tamara Servi)

MC 5403