p-extensões galoisianas e aplicações

Abstract

Let K/Q be an Abelian extension of ood degree ρ and conductor n, where ρ does not ramify in K/Q. The main contributions of this work are: 1) characterization of ideals of Ok whose factorization includes only prime ramified ideals K/Q; 2) calculation of the center density of the geometric representation of Z-modules in Ok characterized by a modular equation (for ρ = 3.5, and 7, the algorithm that is used to optimize the center density of those lattices is parametrized). Besides, the following results are also described: 1) Families of lattices associated to polynomials in Z[x] of degree two and three; 2) an alternative proof of the finiteness of the class group of a number field based solely on sphere packings.