Fast computation of class fields given their norm group

Grenié, Loïc. "Fast computation of class fields given their norm group." Journal de Théorie des Nombres de Bordeaux 20.3 (2008): 707-714. <http://eudml.org/doc/10856>.

@article{Grenié2008,
abstract = {Let $K$ be a number field containing, for some prime $\ell $, the $\ell $-th roots of unity. Let $L$ be a Kummer extension of degree $\ell $ of $K$ characterized by its modulus $\mathfrak\{m\}$and its norm group. Let $K_\mathfrak\{m\}$ be the compositum of degree $\ell $ extensions of $K$ of conductor dividing $\mathfrak\{m\}$. Using the vector-space structure of $\operatorname\{Gal\}(K_\mathfrak\{m\} / K)$, we suggest a modification of the rnfkummer function of PARI/GP which brings the complexity of the computation of an equation of $L$ over $K$ from exponential to linear.},
affiliation = {Università degli Studi di Bergamo Facoltà di Ingegneria viale Marconi 5 24044 Dalmine, ITALY},
author = {Grenié, Loïc},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Kummer extension; rnfkummer function; ray class group; Kummer compositum; norm group},
language = {eng},
number = {3},
pages = {707-714},
publisher = {Université Bordeaux 1},
title = {Fast computation of class fields given their norm group},
url = {http://eudml.org/doc/10856},
volume = {20},
year = {2008},
}

TY - JOUR
AU - Grenié, Loïc
TI - Fast computation of class fields given their norm group
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2008
PB - Université Bordeaux 1
VL - 20
IS - 3
SP - 707
EP - 714
AB - Let $K$ be a number field containing, for some prime $\ell $, the $\ell $-th roots of unity. Let $L$ be a Kummer extension of degree $\ell $ of $K$ characterized by its modulus $\mathfrak{m}$and its norm group. Let $K_\mathfrak{m}$ be the compositum of degree $\ell $ extensions of $K$ of conductor dividing $\mathfrak{m}$. Using the vector-space structure of $\operatorname{Gal}(K_\mathfrak{m} / K)$, we suggest a modification of the rnfkummer function of PARI/GP which brings the complexity of the computation of an equation of $L$ over $K$ from exponential to linear.
LA - eng
KW - Kummer extension; rnfkummer function; ray class group; Kummer compositum; norm group
UR - http://eudml.org/doc/10856
ER -