The Asymptotic Formula in Waring’s Problem
نویسنده
چکیده
We derive a new minor arc bound, suitable for applications associated with Waring’s problem, from Vinogradov’s mean value theorem. In this way, the conjectured asymptotic formula in Waring’s problem is established for sums of s kth powers of natural numbers when k > 6 and s > 2k − 11.
منابع مشابه
Vinogradov’s Mean Value Theorem via Efficient Congruencing
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 particular, the conjectured asymptotic formula in Waring’s problem holds for sums of s kth powers of natural numbers whenever s > 2k + 2k − 3.
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