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Explicit Form of Cassels’ p-adic Embedding Theorem for Number Fields
Published online by Cambridge University Press: 20 November 2018
Abstract
In this paper, we give a general explicit form of Cassels’ $p$-adic embedding theorem for number fields. We also give its refined form in the case of cyclotomic fields. As a byproduct, given an irreducible polynomial
$f$ over
$\mathbb{Z}$, we give a general unconditional upper bound for the smallest prime number
$p$ such that
$f$ has a simple root modulo
$p$.
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- Research Article
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- Copyright © Canadian Mathematical Society 2015
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