On coefficient valuations of Eisenstein polynomials
Matthias Künzer[1]; Eduard Wirsing[2]
- [1] Universität Ulm Abt. Reine Mathematik D-89069 Ulm, Allemagne
- [2] Universität Ulm Fak. f. Mathematik D-89069 Ulm, Allemagne
Journal de Théorie des Nombres de Bordeaux (2005)
- Volume: 17, Issue: 3, page 801-823
- ISSN: 1246-7405
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topKünzer, Matthias, and Wirsing, Eduard. "On coefficient valuations of Eisenstein polynomials." Journal de Théorie des Nombres de Bordeaux 17.3 (2005): 801-823. <http://eudml.org/doc/249444>.
@article{Künzer2005,
abstract = {Let $p\ge 3$ be a prime, let $n > m\ge 1$. Let $\pi _n$ be the norm of $\zeta _\{p^n\} - 1$ under $C_\{p-1\}$, so that $\mathbb\{Z\}_\{(p)\}[\pi _n]|\mathbb\{Z\}_\{(p)\}$ is a purely ramified extension of discrete valuation rings of degree $p^\{n-1\}$. The minimal polynomial of $\pi _n$ over $\mathbb\{Q\}(\pi _m)$ is an Eisenstein polynomial; we give lower bounds for its coefficient valuations at $\pi _m$. The function field analogue, as introduced by Carlitz and Hayes, is studied as well.},
affiliation = {Universität Ulm Abt. Reine Mathematik D-89069 Ulm, Allemagne; Universität Ulm Fak. f. Mathematik D-89069 Ulm, Allemagne},
author = {Künzer, Matthias, Wirsing, Eduard},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
number = {3},
pages = {801-823},
publisher = {Université Bordeaux 1},
title = {On coefficient valuations of Eisenstein polynomials},
url = {http://eudml.org/doc/249444},
volume = {17},
year = {2005},
}
TY - JOUR
AU - Künzer, Matthias
AU - Wirsing, Eduard
TI - On coefficient valuations of Eisenstein polynomials
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2005
PB - Université Bordeaux 1
VL - 17
IS - 3
SP - 801
EP - 823
AB - Let $p\ge 3$ be a prime, let $n > m\ge 1$. Let $\pi _n$ be the norm of $\zeta _{p^n} - 1$ under $C_{p-1}$, so that $\mathbb{Z}_{(p)}[\pi _n]|\mathbb{Z}_{(p)}$ is a purely ramified extension of discrete valuation rings of degree $p^{n-1}$. The minimal polynomial of $\pi _n$ over $\mathbb{Q}(\pi _m)$ is an Eisenstein polynomial; we give lower bounds for its coefficient valuations at $\pi _m$. The function field analogue, as introduced by Carlitz and Hayes, is studied as well.
LA - eng
UR - http://eudml.org/doc/249444
ER -
References
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