Hua's lemma is a result in number theory, particularly in the area of additive number theory, often associated with the work of the Chinese mathematician Hua Luogeng. It generally pertains to the distribution of integers and can be used in problems related to additive representations or counting problems. The lemma can be formulated in terms of a sum over integers, usually involving counting the number of ways an integer can be expressed as a sum of a fixed number of integers from a specific set.
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For and every , the displayed estimate bounds a mean value of a polynomial exponential sum. For cubes its eighth-moment bound is . It complements pointwise Weyl differencing estimates: a ninth moment over a region is bounded by its supremum there times this eighth moment. Leiden lecture notes, Section 8.1 give the cubic formulation.