Abstract
It is shown that each rational approximant to ( ω , ω 2 ) 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 ω 3 + k ω - 1 = 0 or ω 3 + kd ω - d = 0 . A result similar to the main result of Ito et al. [On simultaneous approximation to ( α , α 2 ) with α 3 + k α - 1 = 0 , J. Number Theory 99 (2003) 255–283] is obtained.
Published Version
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