科研之友
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摘要
We develop a substantial enhancement of the efficient congruencing method to estimate Vinogradov's integral of degree k for moments of order 2s, thereby obtaining for the first time near-optimal estimates for s > 5/8k(2). There are numerous applications. In particular, when k is large, the anticipated asymptotic formula in Waring's problem is established for sums of s kth powers of natural numbers whenever s >= 1.543k(2).
- 出版日期2015-9
