Vinogradov's mean value theorem

《複素多様体論 I,II,III》 · 第 59 页 · Section 5.1，Theorem 5.1

Vinogradov's mean value theorem. For each pair of natural numbers $k,l$ there exists a positive number $C(l,k)$ such that for every $X>0$, $J_l^{(k)}(X)\le C(l,k)X^{2l-k(k+1)/2+\eta}$, where $\eta=\frac12k^2(1-1/k)^l$.