Supercritical discrete restriction estimates for forms in many variables

Abstract

We prove discrete restriction estimates for a broad class of hypersurfaces and varieties of intermediate codimension. For our result about hypersurfaces, we use Bourgain's arithmetic version of the Tomas--Stein method and Magyar's decomposition of Birch's hypersurfaces. For our result about varieties of higher codimension, we use the even moment method and works of Birch and Schmidt.

arXiv comment16 pages

References in corpus (10)

• The cubic case of the main conjecture in Vinogradov's mean value theorem
• Diophantine equations in the primes
• On integer solutions of Parsell-Vinogradov systems
• Improved ${\ell }^p$-Boundedness for Integral $k$-Spherical Maximal Functions
• Forms in many variables and differing degrees
• Discrete restriction for $(x,x^3)$ and related topics
• Decoupling for two quadratic forms in three variables: a complete characterization
• A bilinear proof of decoupling for the cubic moment curve
• ${\ell }^p$-improving for discrete spherical averages
• Discrete restriction estimates of epsilon-removal type for kth-powers and k-paraboloids