Y. Tachiya

activity

20162026

most citedAlgebraic independence results for values of Theta-constants, II

1 citations · 1 across the 8 of their papers we have counts for

collaborators

8 papers

math.NT2026

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…

math.NT2025

On the number of $k$ -full integers between three successive $k$ -th powers

Shusei Narumi, Yohei Tachiya

Let $k \geq 2$ be an integer. The aim of this paper is to investigate the distribution of $k$ -full integers between three successive $k$ -th powers. More precisely, for any integers $…

math.NT2023

Linear independence of series related to the Thue--Morse sequence along powers

Michael Coons, Yohei Tachiya

The Thue--Morse sequence ${t (n)}_{n ⩾ 1}$ is the indicator function of the parity of the number of ones in the binary expansion of positive integers $n$ , where $t (n) = 1$ (r…

math.NT2022

Linear independence of certain numbers in the base- $b$ number system

Shintaro Murakami, Yohei Tachiya

Let $(i, j) \in N \times N_{\geq 2}$ and $S_{i, j}$ be an infinite subset of positive integers including all prime numbers in some arithmetic progression. In this pape…

math.NT2020

Algebraic independence of certain infinite products involving the Fibonacci numbers

Daniel Duverney, Yohei Tachiya

Let ${F_{n}}_{n \geq 0}$ 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…

math.NT2019

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…

math.NT2016

Algebraic independence results for values of Jacobi theta-constants

Carsten Elsner, Yohei Tachiya

Let $θ_{3} (τ) = 1 + 2 \sum_{ν = 1}^{\infty} q^{ν^{2}}$ with $q = e^{iπ τ}$ and $ℑ (τ) > 0$ denote the Thetanullwert of the Jacobi theta function \[θ(z|τ) \,=\,\sum_{ν=-\infty}^{\infty} e^{πiν^2τ…

math.NT2016★ 1 cited

Algebraic independence results for values of Theta-constants, II