Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three
By Jean Bourgain, Ciprian Demeter, Larry Guth. 2015
342 citations recorded by the source corpus.
We prove the main conjecture in Vinogradov's Mean Value Theorem for degrees higher than three. This will be a consequence of a sharp decoupling inequality for curves
Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/f41e35205228d460ccd864553b9fe7d8654595cd
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In Computational Mechanics
In Computer Vision and Pattern Recognition
In Numerical Analysis
Citations in the corpus
- Nested efficient congruencing and relatives of Vinogradov's mean value theorem (2017, methodology): “velopments. In §§13 and 14 we record some applications of Theorem 1.1 and its corollaries to Waring’s problem and cognate applications. Several commentators have described the work of Bourgain et al. [8] concerning Vinogradov’s mean value theorem as inherently analytic in nature, contrasting it to e”
- Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds (2018, methodology): “e applied to prove natural variable coefficient extensions of other known decoupling results, such as the ℓ2 decoupling theorem for the paraboloid [8] or the decoupling theorem of Bourgain–Demeter–Guth [11] for the moment curve (in the latter case the relevant variable coefficient operators are those ap”