Dickson's History of the Theory of Numbers, vol II p. 94 refers to some theorems of Kronecker on linear forms:



> 
> ...find integers $w$ and $w^\prime$
>  such that $aw+a^\prime w^\prime$ takes
>  a value as near as possible to $\xi$,
>  where $a$, $a^\prime$ and $\xi$ are
>  given real numbers. In general,
>  consider a system of $p$ equations $$
> > a\_{i,1}w\_1+\dots+a\_{i,q}w\_q=\xi\_i\qquad(i=1,\dots,p),
> > $$ with real coefficients...
> 
> 
> 


Dickson cites Kronecker's *Werke*, which I have, but my German is poor. Hardy and Wright has a chapter on 'Kronecker's Theorem', but not in this generality. I'm actually interested in the case $p=1$ and $\xi\_1=1$; one equation with $q$ integer variables. 


Can anyone suggest a modern reference in English?



Kronecker theorems on linear forms.
Take a look at Cassels - "An intorduction to diophantine approximation", Theorem VI in Ch1, where the theorem that Gerry mentioned is proved.
I'm guessing that it appears also in Siegel's book about the geometry of numbers, although I don't have it with me at the moment.


