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math.NT2011★ 59 cited
Vinogradov's mean value theorem via efficient congruencing, II
Trevor D. Wooley
We apply the efficient congruencing method to estimate Vinogradov's integral for moments of order 2s, with 1<=s<=k^2-1. Thereby, we show that quasi-diagonal behaviour holds when s=…
math.NT2011★ 114 cited
Vinogradov's mean value theorem via efficient congruencing
Trevor D. Wooley
We obtain estimates for Vinogradov's integral which for the first time approach those conjectured to be the best possible. Several applications of these new bounds are provided. In…