This work is concerned with zeta functions of two-dimensional shifts of finite type. A two-dimensional zeta function $zeta^(s)$, which generalizes the Artin-Mazur zeta function, was given by Lind for $mathbb^$-action $phi$. In this paper, the $n$th-order zeta function $zeta_$ of $phi$ on $mathbb_{n imes infty}$, $ngeq 1$, is studied first. The trace operator $mathbf_$, which is the transition matrix for $x$-periodic patterns with period $n$ and height $2$, is rotationally symmetric. The rotational symmetry of $mathbf_$ induces the reduced trace operator $ au_$...
This work is concerned with zeta functions of two-dimensional shifts of finite type. A two-dimensional zeta function $zeta^(s)$, which generalizes ...
