Solution-free sets for sums of binary forms

Prendiville, Sean (2013) Solution-free sets for sums of binary forms. Proceedings of the London Mathematical Society, 107 (2). pp. 267-302. ISSN 0024-6115

Abstract

In this paper, we obtain quantitative estimates for the asymptotic density of subsets of the integer lattice ℤ2 that contain only trivial solutions to an additive equation involving binary forms. In the process we develop an analogue of Vinogradov's mean value theorem applicable to binary forms.