On a binary system of Prendiville: The cubic case

Abstract

We prove sharp decoupling inequalities for a class of two dimensional non-degenerate surfaces in R^5, introduced by Prendiville. As a consequence, we obtain sharp bounds on the number of integer solutions of the Diophantine systems associated with these surfaces.

16 pages; an interpolation was used incorrectly. This error has been fixed in the current version

References in corpus (1)

• On integer solutions of Parsell-Vinogradov systems

Cited by in corpus (2)

• Nested efficient congruencing and relatives of Vinogradov's mean value theorem
• Decoupling for two quadratic forms in three variables: a complete characterization