Lemma Huanum

Lemma Huanum, ex Hua Loo-keng appellatum, in mathematica est aestimatio summarum exponentialium. Quae dicit si res P sit polynomialis per integrales aestimatusFormula:Dubsig gradús k, $\epsilon$ sit numerus realis positivus, et f sit functio realis per

$f(\alpha )=\sum _{x=1}^N\exp (2\pi iP(x)\alpha )$

definita, tum

$\underset{0}{\overset{1}{\int }}|f(\alpha ){|}^{\lambda }d\alpha {\ll }_{P,\epsilon }{N}^{\mu (\lambda )}$,

ubi $(\lambda ,\mu (\lambda ))$ in linea polygonali iacet cum verticibus

$(2^{\nu },2^{\nu }-\nu +\epsilon ),\nu =1,\dots ,k.$