The Dedekind sum [$s(p,q)$](http://en.wikipedia.org/wiki/Dedekind_sum) can be both positive and negative. What are the known lower/upper bounds in terms of p,q? (I would prefer something that grows not faster than q)



On lower/upper bounds for Dedekind sum
For a fixed $q$, the maximum is $$s(1,q)=-{1\over4}+{1\over6q}+{q\over12}$$ and the minimum is $s(q-1,q)=-s(1,q)$. 


