Let K be a cyclic quartic field. Let i(K) denote the index of K. It is known that i(K) ∈ {1, 2, 3, 4, 6, 12}. In Part 1 of this paper we show that i(K) assumes all of these values and we give necessary and sufficient conditions for each to occur. In Part 2 an asymptotic formula is given for the number of cyclic quartic fields with discriminant ≤ x and i(K) = i for each i ∈ {1, 2, 3, 4, 6, 12}.

Additional Metadata
Keywords Cyclic quartic fields, Discriminant, Index
Persistent URL dx.doi.org/10.1007/s00605-002-0547-3
Journal Monatshefte fur Mathematik
Spearman, B.K. (Blair K.), & Williams, K.S. (2003). The Index of a Cyclic Quartic Field. Monatshefte fur Mathematik, 140(1), 19–70. doi:10.1007/s00605-002-0547-3