Year: 2014
Type: preprint
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 $k$-regular sequences, which is introduced by the author [Mi2].
Source: arXiv (Cornell University)
Author: Miyanohara, Eiji
Institution: Waseda University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3170097425