Hankel determinants of the Cantor sequence
Number Theory
2014-11-12 v2 Combinatorics
Abstract
In the paper, we give the recurrent equations of the Hankel determinants of the Cantor sequence, and show that the Hankel determinants as a double sequence is 3-automatic. With the help of the Hankel determinants, we prove that the irrationality exponent of the Cantor number, i.e. the transcendental number with Cantor sequence as its b-ary expansion, equals 2.
Cite
@article{arxiv.1407.3578,
title = {Hankel determinants of the Cantor sequence},
author = {Zhi-xiong Wen and Wen Wu},
journal= {arXiv preprint arXiv:1407.3578},
year = {2014}
}
Comments
20 pages, 1 figure