Integral trace form of extensions of degree pq

Abstract

In this work, we present the integral trace form TrM/Q(x2) of a cyclic extension M/Q with degree pq, where M = KL, p and q are distinct odd primes, the conductor of M is a square free integer, and x belongs to the ring of algebraic integers OM of M. The integral trace form of M/Q allows one to calculate the packing radius of lattices constructed via the canonical (or twisted) homomorphism of submodules of OM