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REMARKS ON EISENSTEIN

Published online by Cambridge University Press:  14 August 2013

YURI BILU  and
ALEXANDER BORICHEV
YURI BILU*
Affiliation:
IMB, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence CEDEX, France
ALEXANDER BORICHEV
Affiliation:
LATP, CMI, Aix-Marseille Université, 39 rue F. Joliot Curie, 13453 Marseille Cedex 13, France
*
✉[email protected]
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Abstract

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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.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 94 , Issue 2 , April 2013 , pp. 158 - 180
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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