Near universal property of a quadratic form of Hessian discriminant 4

Abstract

A quadratic form is universal if it represents all totally positive integers in a number field. In classical number theory over the rational  integers there are some results where a quadratic form takes on all positive integer values except for a certain restricted set. Here we  show that one of the quaternary quadratic forms proven universal for Q( √5) takes on all totally positive values in Q( √2) except for a certain infinite set. The exceptional integers have even norm and the highest power of 2 dividing that norm is 2 to the first power.