The Kloosterman problem for binary Hermitian lattices

Abstract

A Hermitian lattice over an imaginary quadratic field \(\mathbb {Q}(\sqrt{-m})\) is called almost universal if it represents all but finitely many positive integers. We investigate almost universal binary Hermitian lattices and provide a Bochnak-Oh type criterion on almost universality. In particular, all almost universal \(p\)-anisotropic binary Hermitian lattices are universal, and we give the complete list of all such Hermitian lattices.