Let m >= 3 be an integer, zeta(m) is an element of C a primitive mth root of unity, and K-m the cyclotomic field Q(zeta(m)). An explicit description of the integral trace form Tr-Km/Q(x (x) over bar)vertical bar Z[zeta(m)] ...

In this work, we present the integral trace form TrM/Q(x2) of a cyclic extension M/Q with degree pq, where M = KL, p and q are distinct odd primes, the conductor of M is a square free integer, and x belongs to the ring of ...

Let L/Q be a cyclic extension of degree p, where p is an odd unramified prime in L/Q. An explicit description of the integral trace form Tr-L/Q(x(2))|O-L, where O-L is the ring of algebraic integers of L, is given, and an ...

Sejam K e L p-extensões abelianas não ramificadas de condutores livres de quadrados m e n, respectivamente, com p um primo ímpar. O objetivo principal deste trabalho é o de apresentar a Forma Traço Integral nos casos em ...

Os reticulados vem ganhando cada vez mais importância devido às suas aplicações em criptografia e na teoria da informação. Dentre as diversas maneiras de se construir reticulados, uma delas é a construção via extensão de ...

We prove that the integral trace form is a complete invariant for totally real number fields of fundamental discriminant. We also study the relations of this invariant with the trace-zero form and the shape of a number ...

A classification of cubic fields can be done using the trace form and higher analogues of Gauss composition. Using these ideas a new proof for the Scholz reflection principle is given.

A complex trace fossil that requires a three-dimensional (3D) reconstruction is described and interpreted. The specimens studied are assigned to a new ichnospecies (Hillichnus agrioensis) of Hillichnus Bromley et al., 2003. ...