Generalized $k$-regular sequences II:digital pattern and transcendence
Number Theory
2021-12-13 v7
Abstract
In this paper, we prove that an uncountable quantity of real numbers generated by digital pattern sequences gives the transcendental number. This result gives a generalization of Main theorem in Morton and Mourant [MortM], which state that countable real numbers generated by digital pattern sequences gives the transcendental number. Our method relies on the combinatorial quantitative transcendence criterion established by Adamczewski-Bugeaud [AdB2] and the properties of generalized -regular sequences, which is introduced by the author [Mi2].
Cite
@article{arxiv.1405.7124,
title = {Generalized $k$-regular sequences II:digital pattern and transcendence},
author = {Eiji Miyanohara},
journal= {arXiv preprint arXiv:1405.7124},
year = {2021}
}
Comments
We unified arXiv:1405.7124v6 and arXiv:1809.09320v2. Therefore, we replace arXiv:1809.09320v2 by arXiv:1809.09320v3. arXiv:1809.09320v3 now includes arXiv:1405.7124v6