Additive Theory of Prime Numbers

By L. Hua. 2009

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Nested efficient congruencing and relatives of Vinogradov's mean value theorem (2017, methodology): “g method that we outline in §2 now also remedies this NESTED EFFICIENT CONGRUENCING 5 defect. Work prior to 2010 preceding the eﬃcient congruencing methods was, meanwhile, far weaker (see for example [23, 41, 43]). We have already expended considerable space on recording our main conclusions and des”
On the concentration of points of polynomial maps and applications (2012, methodology): “Here we use the approach of [5], combined with estimates on the Vinogradov mean value theorem (see [10, 11, 18] to estimate N(H; K, L).”
Vinogradov's mean value theorem via efficient congruencing, II (2011, background): “tional variables requires some discussion which hints at possible new strategies for transforming estimates for Js,k(X) into upper bounds for Ge(k). En route we also improve some old estimates of Hua [17]. Write g(α) = X 16x6X e(αxk), and when s∈ N, deﬁne Is(X) = Z 1 0 |g(α)|2sdα. Then on considerin”