Small cap decouplings
Name
39_2020_541_ReferencePDF.pdf
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558.92 KB
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0bc9171e6675eb19a3b8d86a1e7577f9
Author(s)
Demeter, Ciprian
Guth, Larry
Wang, Hong
Date Issued
August 6, 2020
Publisher
Springer International Publishing
Version
Author's final manuscript
Abstract
Abstract
We develop a toolbox for proving decouplings into boxes with diameter smaller than the canonical scale. As an application of this new technique, we solve three problems for which earlier methods have failed. We start by verifying the small cap decoupling for the parabola. Then we find sharp estimates for exponential sums with small frequency separation on the moment curve in
$$\mathbb {R}^3$$
R
3
. This part of the work relies on recent improved Kakeya-type estimates for planar tubes, as well as on new multilinear incidence bounds for plates and planks. We also combine our method with the recent advance on the reverse square function estimate, in order to prove small cap decoupling into square-like caps for the two dimensional cone. The Appendix by Roger Heath-Brown contains an application of the new exponential sum estimates for the moment curve, to the Riemann zeta-function.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00039-020-00541-5
