A NEW NUMBER FIELD CONSTRUCTION OF THE $D_4$-LATTICE

Abstract

A classical problem in lattice theory is to determine whether a given lattice can be realized as OK -lattice, where OK is the ring of integers of some number field K. In this work we show that the lattice D4 can be realized as an OF -lattice for infinitely many totally real biquadratic fields F . AMS Subject Classification: 11H06, 11H31, 11R16