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Explicit Form of Cassels’ p-adic Embedding Theorem for Number Fields
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- Journal:
- Canadian Journal of Mathematics / Volume 67 / Issue 5 / 01 October 2015
- Published online by Cambridge University Press:
- 20 November 2018, pp. 1046-1064
- Print publication:
- 01 October 2015
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- Article
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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 $p$.
