It is well known that in general the Jacobi-Perron algorithm (a multi-dimensional analogue of the continued fraction algorithm) may or might not acknowledge the dependence over Q of its arguments l,α_1,...,α_n by truncating itself down to fewer arguments from some step onwards (if so, the algorithm is said to display an 'interruption'). We show here that if n = 2 then 1,α_1,α_2 are linearly dependent over Q if and only if the Jacobi-Perron Algorithm displays an interruption. We give examples showing this is not so for any n ≥ 3.
展开▼
