6 papers · 1 filter
Refinements of Erdős's irrationality criterion for certain sparse infinite series
Hajime Kaneko, Yuta Suzuki, Yohei Tachiya
In this paper, we establish new irrationality criteria for certain sparse power series. As applications of these criteria, we generalize a result of Erdős and obtain several irrati…
On the number of -full integers between three successive -th powers
Shusei Narumi, Yohei Tachiya
Let be an integer. The aim of this paper is to investigate the distribution of -full integers between three successive -th powers. More precisely, for any integers $…
Linear independence of series related to the Thue--Morse sequence along powers
Michael Coons, Yohei Tachiya
The Thue--Morse sequence is the indicator function of the parity of the number of ones in the binary expansion of positive integers , where (r…
Algebraic independence of certain infinite products involving the Fibonacci numbers
Daniel Duverney, Yohei Tachiya
Let be the sequence of the Fibonacci numbers. The aim of this paper is to give explicit formulae for the infinite products \[ \prod_{n=1}^{\infty}\left( 1+\fra…
Linear independence results for certain sums of reciprocals of Fibonacci and Lucas numbers
Daniel Duverney, Yuta Suzuki, Yohei Tachiya
The aim of this paper is to give linear independence results for the values of certain series. As an application, we derive arithmetical properties of the sums of reciprocals of Fi…
Algebraic independence results for values of Theta-constants, II
Carsten Elsner, Yohei Tachiya
Let with denote the Thetanullwert of the Jacobi theta function \[θ(z|τ) \,=\,\sum_{ν=-\infty}^{\infty} e^{πiν^2τ+ 2πiνz} \,.\] M…