Remarks on Eisenstein

Details Remarks on Eisenstein Remarks on Eisenstein

2011-12-10

arxiv.org/abs/1112.2290v2

Mathematics

Number Theory

In Version 2 Section 7 is added and Section 8 (former 7) is modified

Scientific paper

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.

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