In context of analytic numbertheory I am faced with the problem to give an asymptotic estimation for $$C\frac{\vert t\vert^\epsilon}{\log\log \vert t\vert}$$ for a constant $C>0$ and an arbitrary $\epsilon>0$.
It's no problem to see that $$C\frac{\vert t\vert^\epsilon}{\log\log \vert t\vert}=O(\vert t\vert^\epsilon)$$ which makes this denominator $\log \log t$ quite worthless. Now I wonder, if there is any better asymptotic than that? Can we acutally make any use of this denominator? Since we know that $\log t=O(t^\epsilon)$ and therefore $\log\log t=O(t^\epsilon)$ I dont think that there are any better estimations, but I am not so sure about it.
Can anyone help me on this?