12 citations · 65 across the 36 of their papers we have counts for
39 papers
The natural extension of the -transformation
Shigeki Akiyama, Hiromi Ei, Hiroaki Ito
We give a concrete construction of a natural extension of -transformation when is greater than the golden mean. Our construction relies on its Markov diagram and the eige…
Periodic expansion of one by Salem numbers
Shigeki Akiyama, Hachem Hichri
We show that for a Salem number of degree , there exists a positive constant that is a Parry number for integers of natural density . Further, we…
Curious congruences for cyclotomic polynomials
Shigeki Akiyama, Hajime Kaneko
Let be the -th derivative of -th cyclotomic polynomial. Extending a work of D.~H.~Lehmer, we show some curious congruences: is divisible by $ϕ(…
Exponential Diophantine approximation and symbolic dynamics
Shigeki Akiyama, Teturo Kamae, Hajime Kaneko
We extend the key formula which intertwines multiplicative Markoff-Lagrange spectrum and symbolic dynamics. The proof uses complex analysis and elucidates the strategy of the probl…
Width deviation of convex polygons
Shigeki Akiyama, Teturo Kamae
We consider the width of a convex -gon in the plane along the random direction and study its deviation rate: $$ δ(X_T)=\frac{\sqrt{\ma…
Asymptotic formula for balanced words
Shigeki Akiyama
We give asymptotic formulas for the number of balanced words whose slope and intercept lie in a prescribed rectangle. They are related to uniform distribution of Farey frac…