Periods and elementary real numbers
Algebraic Geometry
2008-05-06 v1 Number Theory
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.
Cite
@article{arxiv.0805.0349,
title = {Periods and elementary real numbers},
author = {Masahiko Yoshinaga},
journal= {arXiv preprint arXiv:0805.0349},
year = {2008}
}
Comments
19 pages