Small cap decouplings. With an appendix by D. R. Heath-Brown.

DOI10.1007/s00039-020-00541-5zbMath1454.42008OpenAlexW3048182108MaRDI QIDQ2216456

Hong Wang, Ciprian Demeter, Lawrence Guth

Publication date: 16 December 2020

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00039-020-00541-5

zbMATH Keywords

Riemann zeta-functiondecouplings into boxes with diameter smaller than the canonical scaleKakeya-type estimates for planar tubes

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Harmonic analysis and PDEs (42B37)

Related Items (14)

On 𝐿¹² square root cancellation for exponential sums associated with nondegenerate curves in ℝ⁴ ⋮ Small cap decoupling inequalities: bilinear methods ⋮ An incidence estimate and a Furstenberg type estimate for tubes in \(\mathbb{R}^2\) ⋮ Decoupling for two quadratic forms in three variables: a complete characterization ⋮ An exceptional set estimate for restricted projections to lines in \(\mathbb{R}^3\) ⋮ Decoupling inequalities for quadratic forms ⋮ Real analysis, harmonic analysis and applications. Abstracts from the workshop held July 3--9, 2022 ⋮ Subconvexity in the inhomogeneous cubic Vinogradov system ⋮ A sharp \(L^{10}\) decoupling for the twisted cubic ⋮ Sharp superlevel set estimates for small cap decouplings of the parabola ⋮ Decoupling inequalities for short generalized Dirichlet sequences ⋮ On a free Schrödinger solution studied by Barceló–Bennett–Carbery–Ruiz–Vilela ⋮ Incidence estimates for well spaced tubes ⋮ A bilinear proof of decoupling for the cubic moment curve

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The cubic case of the main conjecture in Vinogradov's mean value theorem
• Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three
• Bounds on oscillatory integral operators based on multilinear estimates
• Decouplings for surfaces in \(\mathbb{R}^4\)
• Decouplings for curves and hypersurfaces with nonzero Gaussian curvature
• Decoupling inequalities and some mean-value theorems
• Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces
• Incidence estimates for well spaced tubes
• A sharp square function estimate for the cone in \(\mathbb{R}^3\)
• On Falconer's distance set problem in the plane
• The proof of the \(l^2\) decoupling conjecture
• A new \(k\)th derivative estimate for exponential sums via Vinogradov's mean value
• Decoupling, exponential sums and the Riemann zeta function
• Decoupling for Perturbed Cones and the Mean Square of $|\zeta (\frac 12+it)|$
• Rational solutions of pairs of diagonal equations, one cubic and one quadratic
• Fourier Restriction, Decoupling, and Applications

This page was built for publication: Small cap decouplings. With an appendix by D. R. Heath-Brown.