O-minimality is a model-theoretic property with uses in number theory and functional transcendence. Many important functions are known to be definable in o-minimal structures when restricted to appropriate domains, including the exponential function, the Klein \(j\) function, and Weierstrass \(\wp\) functions.
I will present joint work with P. Speissegger in which we prove that the Gamma function, which was known to be o-minimal when restricted to the positive real numbers, is in fact o-minimal on certain unbounded complex domains. A similar result holds for the Riemann zeta function.