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arXiv · 1401.6819

Explicit form of Cassels' $p$-adic embedding theorem for number fields

Arturas Dubickas·Min Sha·Igor E. Shparlinski
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Abstract

In this paper, we mainly 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 $Z$, 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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Arturas Dubickas, Min Sha, Igor E. Shparlinski. 2014-10-20. Explicit form of Cassels' $p$-adic embedding theorem for number fields. https://arxiv.org/abs/1401.6819

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