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

2014/01/27 by Arturas Dubickas, Min Sha, Dubickas, Arturas +3
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1401.6819

arxiv created 2014/10/20 · arxiv updated 2014/10/21

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.

Related

• On the p-th root of a p-adic number
• Local Descriptions of Roots of Cubic Equations over P-adic Fields
• A note on generators of number fields
• The exceptional set in Cassel's theorem on small cyclotomic integers
• A note on quadratic cyclotomic extensions