Orthogonal decompositions of integral trace forms of cyclotomic fields and their canonical forms over the ring of p-adic integers

摘要

In this article, we consider integral trace forms of cyclotomic fields given by the restrictions of trace forms TrQ(ζ_n)/Q to and we get orthogonal decompositions of symmetric Z-bilinear modules Oq(ζ_n)into rank one and rank two symmetric Z-bilinear modules in an explicit way. As a result, we can get canonical forms of symmetric ZP-bilinear modules ZP ?z OQ(ζn) over ZP the ring of p-adic integers.