EFFECTIVE l 2 DECOUPLING FOR THE PARABOLA

DOI10.1112/mtk.12038zbMath1442.42032arXiv1711.01202OpenAlexW3023241838MaRDI QIDQ5112999

Zane Kun Li

Publication date: 9 June 2020

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.01202

zbMATH Keywords

moment curve\(l^2L^p\) decouplingparabola decoupling constantsixth-order correlation of integer solutions

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Quadratic and bilinear Diophantine equations (11D09)

Related Items (6)

Decoupling inequalities for quadratic forms ⋮ Sharp variation-norm estimates for oscillatory integrals related to Carleson's theorem ⋮ An \(l^2\) decoupling interpretation of efficient congruencing: the parabola ⋮ On integer solutions of Parsell-Vinogradov systems ⋮ A bilinear proof of decoupling for the cubic moment curve ⋮ A short proof of ℓ2 decoupling for the moment curve

Cites Work

• Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three
• A study guide for the \(l^{2}\) decoupling theorem
• The number of integer points on Vinogradov's quadric
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Nodal length fluctuations for arithmetic random waves
• The proof of the \(l^2\) decoupling conjecture
• On the Vinogradov mean value
• A new \(k\)th derivative estimate for exponential sums via Vinogradov's mean value
• L p regularity of averages over curves and bounds for associated maximal operators
• Zero-free regions for the Riemann zeta function
• VINOGRADOV'S INTEGRAL AND BOUNDS FOR THE RIEMANN ZETA FUNCTION
• A Problem on Sums of Two Squares
• Translation invariance, exponential sums, and Waring's problem
• Nested efficient congruencing and relatives of Vinogradov's mean value theorem

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