Vinogradov's mean value theorem via efficient congruencing, II
By Trevor D. Wooley. 2011
141 citations recorded by the source corpus.
We apply the efficient congruencing method to estimate Vinogradov's integral for moments of order 2s, with 1 =k^2-1. In this way we come half way to proving the main conjecture in two different directions. There are consequences for estimates of Weyl type, and in several allied applications. Thus, for example, the anticipated asymptotic formula in Waring's problem is established for sums of s kth powers of natural numbers whenever s>=2k^2-2k-8 (k>=6).
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/8f46476e13423bb0292301bd99a25228968b8255
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In Algebra and Number Theory
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Citations in the corpus
- Piatetski-Shapiro sequences (2012, unknown): “One can adapt the work of Baker and Kolesnik [7] to give an explicit value for b; an even larger value for b would follow by incorporating the recent work of Wooley [27].”
- Nested efficient congruencing and relatives of Vinogradov's mean value theorem (2017, methodology): “A comparison of the efficient congruencing methods (see especially [48, 55, 57, 60] and the present paper) with the l(2)-decoupling approach [9], however, shows the core of both methods to be strikingly similar.”