The Zeta Function with a 2-Dimensional Shift of Finite Type via Left and Upward Shifts

In this study, we studied the zeta function with a 2-dimensional shift of finite type via left and upward shifts, on a subspace of the space of doubly indexed sequences over a finite abelian compact group and new way to calculate periodic point numbers based on the study of linear algebra of F2 the field and index subgroup. We showed the periodic point data of 2-dimensional shift of finite type via left and upward shifts.