Universal binary positive definite hermitian lattices

Abstract

We will determine all universal integral lattices on binary positive definite Hermitian spaces over arbitrary imaginary quadratic fields, where a positive definite lattice is said to be ‘universal’ if it represents all positive rational integers. A.G. Earnest and A. Khosravani determined universal binary Hermitian lattices when the imaginary quadratic fields have class number 1. In this paper we will extend the result to the case of fields with arbitrary class numbers and obtain nine new universal binary Hermitian lattices up to equivalence, including nonfree lattices. © 2000 Rocky Mountain Mathematics Consortium.