Remarks on Eisenstein
arXiv:1112.2290
Abstract
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.
In Version 2 Section 7 is added and Section 8 (former 7) is modified