Hua's lemma

In mathematics, Hua's lemma,[1] named for Hua Loo-keng, is an estimate for exponential sums.

It states that if P is an integral-valued polynomial of degree k, is a positive real number, and f a real function defined by



where lies on a polygonal line with vertices


  1. ^ Hua Loo-keng (1938). "On Waring's problem". Quarterly Journal of Mathematics. 9 (1): 199–202. doi:10.1093/qmath/os-9.1.199.