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.

We study the problem of constructing and enumerating, for any integers m,n>1, number fields of degree n whose ideal class groups have “large" m-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 m,n>1, des corps de nombres de degré n dont le groupe des classes possède un “grand” m-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.

DOI: 10.5802/jtnb.598
Levin, Aaron 1

1 Centro di Ricerca Matematica Ennio De Giorgi Collegio Puteano Scuola Normale Superiore Piazza dei Cavalieri, 3 I-56100 Pisa, Italy
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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://www.numdam.org/articles/10.5802/jtnb.598/

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