We study the problem of constructing and enumerating, for any integers , number fields of degree whose ideal class groups have “large" -rank. Our technique relies fundamentally on Hilbert’s irreducibility theorem and results on integral points of bounded degree on curves.
Nous étudions la construction et le comptage, pour tout couple d’entiers , des corps de nombres de degré dont le groupe des classes possède un “grand” -rang. Notre technique repose essentiellement sur le théorème d’irréductibilité de Hilbert et sur des résultats concernant les points entiers de degré borné sur des courbes.
@article{JTNB_2007__19_2_485_0, author = {Levin, Aaron}, title = {Ideal class groups, {Hilbert{\textquoteright}s} irreducibility theorem, and integral points of bounded degree on curves}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {485--499}, publisher = {Universit\'e Bordeaux 1}, volume = {19}, number = {2}, year = {2007}, doi = {10.5802/jtnb.598}, mrnumber = {2394898}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/jtnb.598/} }
TY - JOUR AU - Levin, Aaron TI - Ideal class groups, Hilbert’s irreducibility theorem, and integral points of bounded degree on curves JO - Journal de théorie des nombres de Bordeaux PY - 2007 SP - 485 EP - 499 VL - 19 IS - 2 PB - Université Bordeaux 1 UR - http://archive.numdam.org/articles/10.5802/jtnb.598/ DO - 10.5802/jtnb.598 LA - en ID - JTNB_2007__19_2_485_0 ER -
%0 Journal Article %A Levin, Aaron %T Ideal class groups, Hilbert’s irreducibility theorem, and integral points of bounded degree on curves %J Journal de théorie des nombres de Bordeaux %D 2007 %P 485-499 %V 19 %N 2 %I Université Bordeaux 1 %U http://archive.numdam.org/articles/10.5802/jtnb.598/ %R 10.5802/jtnb.598 %G en %F JTNB_2007__19_2_485_0
Levin, Aaron. Ideal class groups, Hilbert’s irreducibility theorem, and integral points of bounded degree on curves. Journal de théorie des nombres de Bordeaux, Volume 19 (2007) no. 2, pp. 485-499. doi : 10.5802/jtnb.598. http://archive.numdam.org/articles/10.5802/jtnb.598/
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