REMARKS ON EISENSTEIN-Reference-Cited by-同舟云学术

REMARKS ON EISENSTEIN

Published:2013-04 Issue:2 Volume:94 Page:158-180
ISSN:1446-7887
Container-title:Journal of the Australian Mathematical Society
language:en
Short-container-title:J. Aust. Math. Soc.

Author:

BILU YURI,BORICHEV ALEXANDER

Abstract

AbstractWe 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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference20 articles.

1. Lower bounds for height functions

2. Construction and estimation of bases in function fields

3. Eisenstein's theorem on power series expansions of algebraic functions

4. ESTIMATES FOR THE SOLUTIONS OF CERTAIN DIOPHANTINE EQUATIONS BY RUNGE'S METHOD

5. On the global distance between two algebraic points on a curve

Cited by 6 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. The local dimension of a finite group over a number field;Transactions of the American Mathematical Society;2022-04-21

2. An upper bound for the number of $S$-integral points on curves of genus zero;Colloquium Mathematicum;2022

3. Binary polynomial power sums vanishing at roots of unity;Acta Arithmetica;2021

4. RETRACTED ARTICLE: Integral points on curves of genus zero over totally real number fields;Periodica Mathematica Hungarica;2020-06-03

5. Chevalley–Weil theorem and subgroups of class groups;Israel Journal of Mathematics;2018-06