A proof of Liouville's theorem via o-minimality

2017/12/19 by Pablo Cubides Kovacsics, Kovacsics, Pablo Cubides · 1 citation
Mathematics · #03C64 #97I80 #Advanced Topology and Set Theory #Complex Variables (math.CV) #FOS: Mathematics #Functional Equations Stability Results #Logic (math.LO) #Meromorphic and Entire Functions #math.CV #math.LO #msc:03C64 #msc:97I80

paper · pdf · doi:10.48550/arxiv.1712.07593

2 pages

arxiv created 2017/12/19 · openalex publication_date 2017/12/19 · arxiv updated 2017/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this short note we give a proof of Liouville's theorem (every bounded entire complex function is constant) following Peterzil and Starchenko's approach to complex analysis via o-minimality.

Cited by

• Some extensive discussions of Liouville's theorem and Cauchy's integral theorem on structural holomorphic

Related

• To the Liouville theorem for entire functions of finite order
• A Liouville Theorem for the Fractional Laplacian
• Some Simplifications in Basic Complex Analysis
• The theory of Liouville functions
• The Liouville function in short intervals [after Matomaki and Radziwill]