Periods and elementary real numbers

Details Periods and elementary real numbers Periods and elementary real numbers

2008-05-03

arxiv.org/abs/0805.0349v1

Mathematics

Algebraic Geometry

19 pages

Scientific paper

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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