Hua's lemma

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

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

then

where ${\displaystyle (\lambda ,\mu (\lambda ))}$ lies on a polygonal line with vertices

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