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Mean value estimates for Weyl sums in two dimensions

Jean Bourgain, Ciprian Demeter

Abstract

We use decoupling theory to estimate the number of solutions for quadratic and cubic Parsell--Vinogradov systems in two dimensions.

Mean value estimates for Weyl sums in two dimensions

Abstract

We use decoupling theory to estimate the number of solutions for quadratic and cubic Parsell--Vinogradov systems in two dimensions.

Paper Structure

This paper contains 11 sections, 24 theorems, 193 equations.

Table of Contents

  1. Introduction
  2. Number theoretical consequences
  3. Parsell--Vinogradov systems
  4. Perturbed manifolds
  5. A Brascamp--Lieb inequality
  6. Transversality
  7. The multilinear restriction theorem
  8. The main inequality
  9. Rescaling
  10. Linear versus multilinear decoupling
  11. The proof of Theorem

Key Result

Theorem 1.1

Theorems & Definitions (30)

  • Theorem 1.1
  • Conjecture 1.2
  • Theorem 2.1
  • Theorem 2.2
  • Corollary 2.3
  • Corollary 2.4
  • Theorem 3.1
  • Theorem 3.2
  • Lemma 4.1
  • Conjecture 4.2
  • ...and 20 more