On optimal simultaneous rational approximation to (ω,ω2)τ with ω being some kind of cubic algebraic function

It is shown that each rational approximant to (ω,ω2)τ given by the Jacobi–Perron algorithm (JPA) or modified Jacobi–Perron algorithm (MJPA) is optimal, where ω is an algebraic function (a formal Laurent series over a finite field) satisfying ω3+kω-1=0 or ω3+kdω-d=0. A result similar to the main result of Ito et al. [On simultaneous approximation to (α,α2) with α3+kα-1=0, J. Number Theory 99 (2003) 255–283] is obtained.