Ideal class groups, Hilbert’s irreducibility theorem, and integral points of bounded degree on curves

Aaron Levin[1]

  • [1] Centro di Ricerca Matematica Ennio De Giorgi Collegio Puteano Scuola Normale Superiore Piazza dei Cavalieri, 3 I-56100 Pisa, Italy

Journal de Théorie des Nombres de Bordeaux (2007)

  • Volume: 19, Issue: 2, page 485-499
  • ISSN: 1246-7405

Abstract

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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.

How to cite

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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 19.2 (2007): 485-499. <http://eudml.org/doc/249974>.

@article{Levin2007,
abstract = {We study the problem of constructing and enumerating, for any integers $m,n&gt;1$, 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.},
affiliation = {Centro di Ricerca Matematica Ennio De Giorgi Collegio Puteano Scuola Normale Superiore Piazza dei Cavalieri, 3 I-56100 Pisa, Italy},
author = {Levin, Aaron},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
number = {2},
pages = {485-499},
publisher = {Université Bordeaux 1},
title = {Ideal class groups, Hilbert’s irreducibility theorem, and integral points of bounded degree on curves},
url = {http://eudml.org/doc/249974},
volume = {19},
year = {2007},
}

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
PB - Université Bordeaux 1
VL - 19
IS - 2
SP - 485
EP - 499
AB - We study the problem of constructing and enumerating, for any integers $m,n&gt;1$, 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.
LA - eng
UR - http://eudml.org/doc/249974
ER -

References

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