6 papers
An extension of algebraic independence of special values for non-lacunary power series
Hajime Kaneko, Satoru Oshima, Takafumi Tsurumaki
We study the algebraic independence of special values of power series , where is a fixed Pisot or Salem number. In particular, we consider the case where $f(X)=\sum_…
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…
Borel Complexity of the set of vectors normal for a fixed recurrence sequence
Hajime Kaneko, Bill Mance
In this paper, we consider recurrence sequences () with companion polynomial . For example, the sequence $x_n=ξ_1(4+\sqrt{2})^n+ξ_2(4-…
On the irrationality exponent of real numbers with low complexity expansion
Yann Bugeaud, Hajime Kaneko, Dong Han Kim
Let be a real number and an integer. We study the relationship between the irrationality exponent of and the subword complexity of the -ary…
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…
Markoff-Lagrange spectrum of one-sided shifts
Hajime Kaneko, Wolfgang Steiner
For the Lagrange spectrum and other applications, we determine the smallest accumulation point of binary sequences that are maximal in their shift orbits. This problem is trivial f…