The theory of Liouville functions

2002/03/12 by Pascal Koiran, Koiran, Pascal
Computer Science · Mathematics · Physics and Astronomy · #03C60 (Primary) #30B10 (Secondary) #Advanced Mathematical Theories and Applications #Advanced Optimization Algorithms Research #Complex Variables (math.CV) #FOS: Mathematics #Logic (math.LO) #Polynomial and algebraic computation #math.CV #math.LO #msc:03C60 #msc:30B10

paper · pdf · doi:10.48550/arxiv.math/0203108

14 pages

arxiv created 2002/03/12 · openalex publication_date 2002/03/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A Liouville function is a complex analytic function H with a Taylor series ∑_n=1^∞ xⁿ/a_n such the a_n's form a ``very fast growing'' sequence of integers. In this paper we exhibit the complete first-order theory of the complex field expanded with H.

Related

• Short Sums of the Liouville Function over Function Fields
• The Dirichlet Series for the Liouville Function and the Riemann Hypothesis
• On Correlations of Liouville-like Functions
• On the Liouville function in short intervals
• Liouville numbers, Liouville sets and Liouville fields