General Definition
Given an integer n > 1, let H be any subgroup of the multiplicative group
of invertible residues modulo n, and let
A Gaussian period P is a sum of the primitive n-th roots of unity, where runs through all of the elements in a fixed coset of H in G.
The definition of P can also be stated in terms of the field trace. We have
for some subfield L of Q(ζ) and some j coprime to n. This corresponds to the previous definition by identifying G and H with the Galois groups of Q(ζ)/Q and Q(ζ)/L, respectively. The choice of j determines the choice of coset of H in G in the previous definition.
Read more about this topic: Gaussian Period
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