The conductor of a cyclic quartic field using Gauss sums

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Let Q denote the field of rational numbers. Let K be a cyclic quartic extension of Q. It is known that there are unique integers A, B, C, D such thatwhereThe conductor ƒ(K) of K is ƒ(K) = 2l|A|D, whereA simple proof of this formula for ƒ (K) is given, which uses the basic properties of quartic Gauss sums.

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