# Waring's problem

What is the best known quantitative upper bound for the quantity $G(k)$?

I know that it's due to Trevor Wooley and in simplest form states that $\limsup_{k \to \infty} \frac{G(k)}{k \log k} \le 1$.

I have been digging mathsci.net and I'm not able to find it.

At Trevor's website, I see $$G(k)\le k(\log k+\log\log k+2+o(1))$$