Hua's lemma - Alchetron, The Free Social Encyclopedia

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, ε is a positive real number, and f a real function defined by

f ( α ) = ∑ x = 1 N exp ⁡ ( 2 π i P ( x ) α ) ,

then

∫ 0 1 | f ( α ) | λ d α ≪ P , ε N μ ( λ ) ,

where ( λ , μ ( λ ) ) lies on a polygonal line with vertices

( 2 ν , 2 ν − ν + ε ) , ν = 1 , … , k .

References

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