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
Famous quotes containing the words general and/or definition:
“We will win this war because we are willing to sacrifice 10,000,000 lives. How many lives is the White Man willing to sacrifice?”
—Jerome Cady, U.S. screenwriter, and Lewis Milestone. General Mitsubi (Richard Loo)
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)