Low functions of reals

2009/03/09 by Katrin Tent, Martin Ziegler, Tent, Katrin +1
Computer Science · Mathematics · #03D20 #Benford’s Law and Fraud Detection #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.0903.1384

openalex publication_date 2009/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new notion of computable function on \R^N and prove some basic properties. We give two applications, first a short proof of Yoshinaga's theorem that periods are \el (they are actually low). We also show that the low complex numbers form a algebraically closed field closed under exponentiation and some other special functions.

Related

• Periods and elementary real numbers
• Fields with pseudo-exponentiation
• On the Complexity of Real Functions
• Periods And Real Numbers
• Computability of Brjuno-like functions