科研之友
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摘要
We apply multigrade efficient congruencing to estimate Vinogradov's integral of degree k for moments of order 2s, establishing strongly diagonal behaviour for 1 <= s <= 1/2k(k+1) -1/3 k+o (k). In particular, as k -> infinity, we confirm the main conjecture in Vinogradov's mean value theorem for a proportion asymptotically approaching 100% of the critical interval 1 <= s <= 1/2k(k + 1).
- 出版日期2017-1
