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When is a 2-Power Cyclotomic Extension cyclic?

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arxiv 2308.08865 v2 pith:GJAFQIIV submitted 2023-08-17 math.NT

Sophie Marques , Elizabeth Mrema This is my paper · ORCID
classification math.NT
keywords cyclotomicpowerbasecharacterizesconditionscycliccyclicitydecompositions
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abstract

This paper characterizes the cyclicity property of $2$-power cyclotomic extensions through various means: the structure of the Galois groups, the nature of their subextensions, tower decompositions, and, most importantly, specific conditions on the base field.

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Cited by 1 Pith paper

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  1. A study of a recursive sequence of polynomials revealing weighted Catalan Numbers

    math.CO 2025-01 conditional novelty 4.0 of 10

    Certain diagonal invariants of the iterated polynomial sequence p_n(x) = p_{n-1}(x)^2 - 2 are shown to be weighted Catalan tree sums, equal in closed form to 2(-1)^k/(2k)!.

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