An introduction to oddly tame number fields

It follows from generalities of quadratic forms that the spinor class of the integral trace of a number field determines the signature and the discriminant of the field. In this paper we define a family of number fields, that contains among others all odd degree Galois tame number fields, for which the converse is true. In other words, for a number field K in such family we prove that the spinor class of the integral trace carries no more information about K than the discriminant and the signature do.