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

Abstract

In this work, we computate the trace form Tr k/Q (x2) associated to a cyclic number field of odd prime degree p, where p ramified in and x belongs to the ring of integers of . 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