2011/12/10 by Yuri Bilu, Alexander Borichev, Bilu, Yuri +1 · 1 citation
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.1112.2290
In Version 2 Section 7 is added and Section 8 (former 7) is modified
arxiv created 2011/12/21 · arxiv updated 2011/12/22
We obtain a fully explicit quantitative version of the Eisenstein theorem on algebraic power series which is more suitable for certain applications than the existing version due to Dwork, Robba, Schmidt and van der Poorten. We also treat ramified series and Laurent series, and we demonstrate some applications; for instance, we estimate the discriminant of the number field generated by the coefficients.