2008/05/03 by Masahiko Yoshinaga, Yoshinaga, Masahiko · 1 voice · 1 citation
Computer Science · Mathematics · #11J17 #68Q15 #Algebraic Geometry (math.AG) #Computability, Logic, AI Algorithms #FOS: Mathematics #Number Theory (math.NT) #Numerical Methods and Algorithms #math.AG #math.NT #msc:11J17 #msc:68Q15 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0805.0349
19 pages
arxiv created 2008/05/03 · openalex publication_date 2008/05/03 · arxiv published 2008/05/03 · arxiv updated 2008/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The periods, introduced by Kontsevich and Zagier, form a class of complex numbers which contains all algebraic numbers and several transcendental quantities. Little has been known about qualitative properties of periods. In this paper, we compare the periods with hierarchy of real numbers induced from computational complexities. In particular we prove that periods can be effectively approximated by elementary rational Cauchy sequences. As an application, we exhibit a computable real number which is not a period.