## Normal regular Hermitian lattices over imaginary quadratic fields

### Volume 179 / 2017

Acta Arithmetica 179 (2017), 37-53
MSC: Primary 11E39; Secondary 11E08.
DOI: 10.4064/aa8582-10-2016
Published online: 28 April 2017

#### Abstract

A positive definite Hermitian lattice over an imaginary quadratic field is called regular if it represents every number represented by its genus. It is called universal if it represents all positive integers. We show that every primitive normal regular integral lattice over a fixed imaginary quadratic field is actually universal if and only if the field discriminant is not 4, 8, 11, 23 and is prime to $3\cdot 5\cdot 7$.