On integer solutions of Parsell-Vinogradov systems

Abstract

We prove a sharp upper bound on the number of integer solutions of the Parsell-Vinogradov system in every dimension $d\ge 2$.

arXiv comment55 pages

References in corpus (14)

• The cubic case of the main conjecture in Vinogradov's mean value theorem
• Nested efficient congruencing and relatives of Vinogradov's mean value theorem
• Vinogradov's mean value theorem via efficient congruencing
• Stability of the Brascamp-Lieb constant and applications
• Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three
• Vinogradov's mean value theorem via efficient congruencing, II
• A short proof of the multilinear Kakeya inequality
• Mean value estimates for odd cubic Weyl sums
• A local smoothing estimate in higher dimensions
• Approximating the main conjecture in Vinogradov's mean value theorem
• Burgess bounds for short mixed character sums
• Decouplings for surfaces in R^4
• Effective $l^2$ decoupling for the parabola
• Sharp decouplings for three dimensional manifolds in ${\mathbb{R}}^5$

Cited by in corpus (12)

• Decoupling for moment manifolds associated to Arkhipov--Chubarikov--Karatsuba systems
• Decoupling for certain quadratic surfaces of low co-dimensions
• Decoupling for two quadratic forms in three variables: a complete characterization
• Strichartz estimates for the Schroedinger equation on non-rectangular two-dimensional tori
• Decoupling inequalities for quadratic forms
• On a binary system of Prendiville: The cubic case
• Regularized Brascamp--Lieb inequalities
• An Algebraic Brascamp-Lieb Inequality
• Large sieve estimate for multivariate polynomial moduli and applications
• Equality in Liakopoulos's generalized dual Loomis-Whitney inequality via Barthe's Reverse Brascamp-Lieb inequality
• Burgess bounds for short character sums evaluated at forms II: the mixed case
• Supercritical discrete restriction estimates for forms in many variables