Proof of the Hyperplane Zeros Conjecture of Lagarias and Wang

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125414We prove that a real analytic subset of a torus group that is contained in its image under an expanding endomorphism is a finite union of translates of closed subgroups. This confirms the hyperplane zeros conjecture of Lagarias and Wang for real analytic varieties. Our proof uses real analytic geometry, topological dynamics and Fourier analysis.25 pagesAlgebraic GeometryDynamical Systems32C05 (Primary); 37B05, 43A40 (Secondary)Proof of the Hyperplane Zeros Conjecture of Lagarias and Wangtext