Trace form associated to cyclic number fields of ramified odd prime degree

摘要

In this work, we computate the trace form Tr-K/Q(x(2)) associated to a cyclic number field K of odd prime degree p, where p ramified in K and x belongs to the ring of integers of K. Furthermore, we use this trace form to calculate the expression of the center density of algebraic lattices constructed via the Minkowski embedding from some ideals in the ring of integers of K.