Explicit form of Cassels' $p$-adic embedding theorem for number fields
Number Theory
2014-10-21 v2
Abstract
In this paper, we mainly give a general explicit form of Cassels' -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 over , we give a general unconditional upper bound for the smallest prime number such that has a simple root modulo .
Keywords
Cite
@article{arxiv.1401.6819,
title = {Explicit form of Cassels' $p$-adic embedding theorem for number fields},
author = {Arturas Dubickas and Min Sha and Igor E. Shparlinski},
journal= {arXiv preprint arXiv:1401.6819},
year = {2014}
}