Definability of complex functions in o‐minimal structures
Abstract
Abstract We prove that holomorphic continuations of functions in the classes and are definable in the o‐minimal structures and , respectively. More specifically, we give complex domains on which the holomorphic continuations are definable and show that these domains are optimal. As an application, we describe optimal domains on which the Riemann zeta function is definable in o‐minimal expansions of and on which the Euler gamma function is definable in o‐minimal expansions of .
Fields of Study & Subjects
Advanced Topology and Set Theory
Advanced Algebra and Logic
Logic
Reasoning
and Knowledge
Publication details
- Journal / source
- Journal of the London Mathematical Society
- Volume
- 114
- Issue
- 1
- Publication date
- 1 July 2026
- Language
- EN