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Periods and elementary real numbers

2008/05/03 by Masahiko Yoshinaga, Yoshinaga, Masahiko
Computer Science · #11J17 #68Q15 #Algebraic Geometry (math.AG) #Computability, Logic, AI Algorithms #FOS: Mathematics #Number Theory (math.NT) #Numerical Methods and Algorithms #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0805.0349

openalex publication_date 2008/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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