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A characterization of Eisenstein polynomials generating extensions of degree $p^{2}$ and cyclic of degree $p^{3}$ over an unramified $𝔭$ -adic field

Maurizio Monge — 2014

Journal de Théorie des Nombres de Bordeaux

Let $p \neq 2$ be a prime. We derive a technique based on local class field theory and on the expansions of certain resultants allowing to recover very easily Lbekkouri’s characterization of Eisenstein polynomials generating cyclic wild extensions of degree $p^{2}$ over $ℚ_{p}$ , and extend it to when the base fields $K$ is an unramified extension of $ℚ_{p}$ . When a polynomial satisfies a subset of such conditions the first unsatisfied condition characterizes the Galois group of the normal closure. We derive a complete...

An equivalent of Kronecker's theorem for powers of an algebraic number and structure of linear recurrences of fixed length

Nevio Dubbini; Maurizio Monge — 2012

Acta Arithmetica

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A characterization of Eisenstein polynomials generating extensions of degree p 2 and cyclic of degree p 3 over an unramified 𝔭 -adic field

An equivalent of Kronecker's theorem for powers of an algebraic number and structure of linear recurrences of fixed length

A characterization of Eisenstein polynomials generating extensions of degree $p^{2}$ and cyclic of degree $p^{3}$ over an unramified $𝔭$ -adic field