Abstract:Let ℓ > 2 be a positive integer, ζ ℓ a primitive ℓ-th root of unity, and K a number field containing ζ ℓ + ζ −1 ℓ but not ζ ℓ . In a recent paper, Chonoles et. al. study iterated towers of number fields over K generated by the generalized Rikuna polynomial, rn(x, t; ℓ) ∈ K(t) [x]. They note that when K = Q, t ∈ {0, 1}, and ℓ = 3, the only ramified prime in the resulting tower is 3, and they ask under what conditions is the number of ramified primes small. In this paper, we apply a theorem of Guàrdia, Montes, a… Show more
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