Let be a prime, let . Let be the norm of under , so that is a purely ramified extension of discrete valuation rings of degree . The minimal polynomial of over is an Eisenstein polynomial; we give lower bounds for its coefficient valuations at . The function field analogue, as introduced by Carlitz and Hayes, is studied as well.
Soit un nombre premier et soient . Soit la norme de sous . Ainsi est une extension purement ramifiée d’anneaux de valuation discrète de degré . Le polynôme minimal de sur est un polynôme de Eisenstein ; nous donnons des bornes inférieures pour les -valuations de ses coefficients. L’analogue dans le cas d’un corps de fonctions, comme introduit par Carlitz et Hayes, est etudié de même.
DOI: 10.5802/jtnb.522
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@article{JTNB_2005__17_3_801_0, author = {Matthias K\"unzer and Eduard Wirsing}, title = {On coefficient valuations of {Eisenstein} polynomials}, journal = {Journal de Th\'eorie des Nombres de Bordeaux}, pages = {801--823}, publisher = {Universit\'e Bordeaux 1}, volume = {17}, number = {3}, year = {2005}, doi = {10.5802/jtnb.522}, zbl = {05016589}, mrnumber = {2212127}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.522/} }
TY - JOUR TI - On coefficient valuations of Eisenstein polynomials JO - Journal de Théorie des Nombres de Bordeaux PY - 2005 DA - 2005/// SP - 801 EP - 823 VL - 17 IS - 3 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.522/ UR - https://zbmath.org/?q=an%3A05016589 UR - https://www.ams.org/mathscinet-getitem?mr=2212127 UR - https://doi.org/10.5802/jtnb.522 DO - 10.5802/jtnb.522 LA - en ID - JTNB_2005__17_3_801_0 ER -
Matthias Künzer; Eduard Wirsing. On coefficient valuations of Eisenstein polynomials. Journal de Théorie des Nombres de Bordeaux, Volume 17 (2005) no. 3, pp. 801-823. doi : 10.5802/jtnb.522. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.522/
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