On effective irrationality exponents of cubic irrationals

We provide an upper bound for the effective irrationality exponents of cubic algebraics x with the minimal polynomial x^3 - tx^2 - a . In particular, we show that it becomes non-trivial, i.e. better than the classical bound of Liouville, in the case |t| > 19.71 a^4/3 . Moreover, under the condition |t| > 86.58 a^4/3 , we provide an explicit lower bound for the expression ||qx|| for all large q∈ℤ . These results are based on the recently discovered continued fractions of cubic irrationals and improve the currently best-known bounds of Wakabayashi.