On the computation of all extensions of a 𝑝-adic field of a given degree

Pauli, Sebastian; Roblot, Xavier-François

doi:10.1090/S0025-5718-01-01306-0

On the computation of all extensions of a $p$-adic field of a given degree
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by Sebastian Pauli and Xavier-François Roblot PDF

Math. Comp. 70 (2001), 1641-1659 Request permission

Abstract:

Let $\mathbf {k}$ be a $p$-adic field. It is well-known that $\mathbf {k}$ has only finitely many extensions of a given finite degree. Krasner has given formulae for the number of extensions of a given degree and discriminant. Following his work, we present an algorithm for the computation of generating polynomials for all extensions $\mathbf {K}/\mathbf {k}$ of a given degree and discriminant.

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