Hajime Kaneko

collaborators

4 papers

math.NT2026

Rotational beta expansions and Schmidt games

Hajime Kaneko, Jonathan Caalim, Nathaniel Nollen

We consider rotational beta expansions in dimensions 1, 2 and 4 and view them as expansions on real numbers, complex numbers, and quaternions, respectively. We give sufficient cond…

math.NT2026

On the irrationality exponent of real numbers with low complexity expansion

Yann Bugeaud, Hajime Kaneko, Dong Han Kim

Let $I^¾$ be a real number and $b \geq 2$ an integer. We study the relationship between the irrationality exponent of $I^¾$ and the subword complexity $p (n, x)$ of the $b$ -ar…

math.NT2026

Refinements of ErdÅs'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 ErdÅs and obtain several irrat…

math.LO2025

Borel Complexity of the set of vectors normal for a fixed recurrence sequence

Hajime Kaneko, Bill Mance

In this paper, we consider recurrence sequences $x_{n} = I^¾_{1} I^\pm_{1}^{n} + I^¾_{2} I^\pm_{2}^{n}$ ( $n = 0, 1, \dots$ ) with companion polynomial $P (X)$ . For example, the sequence $x_n=Î¾_1(4+\sqrt{2})^n+Î…

Rotational beta expansions and Schmidt games

On the irrationality exponent of real numbers with low complexity expansion

Refinements of ErdÅs's irrationality criterion for certain sparse infinite series

Borel Complexity of the set of vectors normal for a fixed recurrence sequence

Refinements of ErdÅs's irrationality criterion for certain sparse infinite series