2 citations · 3 across the 5 of their papers we have counts for
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Digital pattern and transcendence via generalized -regular sequences
Eiji Miyanohara
In this paper, we prove that there are uncountable many real transcendental numbers, which are generated by digital pattern sequences. This generalizes the main theorem in Morton a…
Generalized -regular sequences III: Arithmetical properties of generalized -regular series
Eiji Miyanohara
Let be a -regular series in and be an integer with . Bell, Bugeaud and Coons [BelBC] proved that is either rational or trans…
Transcendence of digital expansions and continued fractions generated by a cyclic permutation and -adic expansion
Eiji Miyanohara
In this article, first we generalize the Thue-Morse sequence (the generalized Thue-Morse sequences) by a cyclic permutation and -adic expansion of natural…
Generalized -regular sequences II:digital pattern and transcendence
Eiji Miyanohara
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 M…
Study on the non-periodicity of the generalized Thue-Morse sequences generated by cyclic permutations
Eiji Miyanohara
First we generalize the Thue-Morse sequence (the generalized Thue-Morse sequences) by a cyclic permutations and p-adic system, and consider the necessary-sufficient condition that…