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The conductor of a cyclic quartic field using Gauss sums. (English) Zbl 0898.11041
This paper presents a new simple proof of the known expression for the conductor of a cyclic quartic extension of the rational field. The proof uses the known properties of quartic Gauss sums.
Reviewer: L.Skula (Brno)

MSC:
11R16 Cubic and quartic extensions
11L05 Gauss and Kloosterman sums; generalizations
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References:
[1] K. Hardy, R.H. Hudson, D. Richman, K.S. Williams and N.M. Holtz: Calculation of the class numbers of imaginary cyclic quartic fields. Carleton-Ottawa Mathematical Lecture Note Series (Carleton University, Ottawa, Ontario, Canada), Number 7, July 1986, pp. 201. · Zbl 0615.12009
[2] K. Ireland and M. Rosen: A Classical Introduction to Modern Number Theory. Springer-Verlag, New York, Second Edition (1990). · Zbl 0712.11001
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