Hua's lemma
Encyclopedia
In mathematics
, Hua's lemma, named for Hua Loo-keng, is an estimate for exponential sum
s.
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
then
,
where
lies on a polygonal line with vertices
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, Hua's lemma, named for Hua Loo-keng, is an estimate for exponential sum
Exponential sum
In mathematics, an exponential sum may be a finite Fourier series , or other finite sum formed using the exponential function, usually expressed by means of the functione = \exp.\,...
s.
It states that if P is an integral-valued polynomial of degree k,
is a positive real number, and f a real function defined bythen
,where
lies on a polygonal line with vertices