Subconvexity for additive equations: pairs of undenary cubic forms

TL;DR

This paper proves that for certain pairs of diagonal cubic equations with at least 11 variables, the number of integral solutions in a large box matches the expected order of magnitude, advancing understanding of additive Diophantine equations.

Contribution

It establishes a lower bound matching the expected count for solutions of specific additive cubic systems with many variables, a new result in the field.

Findings

Number of solutions matches expected order for systems with 11+ variables

Advances subconvexity bounds for additive equations

Provides new techniques for analyzing diagonal cubic forms

Abstract

We investigate pairs of diagonal cubic equations with integral coefficients. For a class of such Diophantine systems with 11 or more variables, we are able to establish that the number of integral solutions in a large box is at least as large as the expected order of magnitude.