'Kronecker' or 'Weyl' sequence?

I am puzzled about the name of an s-dimensional point sequence.
The sequence is usually written down as

{n*alpha} for n=0,1,2,...

where the brackets denote taking the fractional part and alpha is
an s-dimensional vector.

I have seen publications where this sequence is called the
'Kronecker sequence', and I have seen publications where this
sequence is called 'Weyl sequence'.

I think the difference in naming is in the condition on
the s-dimensional vector alpha:

A) If alpha is an s-dimensional vector of real numbers, then i
*think* the sequence should be called 'Kronecker sequence'.

B) If 1, alpha_1, ..., alpha_s are linearly independent over the
rationals (and thus alpha is an s-dimensional vector of irrationals),
then I *think* one should speak of the 'Weyl sequence'.


Can somebody clarify this or point me to some references in the
literature?

I already have a copy of 'Ueber die Gleichverteilung von Zahlen
mod. Eins' von Hermann Weyl... but i don't know the name of the
original paper by Kronecker in which he studies the seqences
{n*alpha}. :-(


Thanks for your advice,
Bart

--
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