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Infinite class field tower with small root discriminant
Published 2 Jun 2024 in math.NT | (2406.00797v2)
Abstract: We generalize Schoof's theorem in 1986 and apply this to construct a class of Kummer extensions of the cyclotomic fields with infinite class tower. As an application, we give some number fields with a small root discriminant, which has an infinite $p$-class field tower when $p=3, 5, 7$.
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