Asymptotics of number fields and the Cohen–Lenstra heuristics
J. Klüners, Journal de Théorie Des Nombres de Bordeaux 18 (2006) 607–615.
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We study the asymptotics conjecture of Malle for dihedral groups Dℓ of order 2ℓ, where ℓ is an odd prime. We prove the expected lower bound for those groups. For the upper bounds we show that there is a connection to class groups of quadratic number fields. The asymptotic behavior of those class groups is predicted by the Cohen--Lenstra heuristics. Under the assumption of this heuristic we are able to prove the expected upper bounds.
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Journal de Théorie des Nombres de Bordeaux
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18
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3
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607-615
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Klüners J. Asymptotics of number fields and the Cohen–Lenstra heuristics. Journal de Théorie des Nombres de Bordeaux. 2006;18(3):607-615. doi:10.5802/jtnb.561
Klüners, J. (2006). Asymptotics of number fields and the Cohen–Lenstra heuristics. Journal de Théorie Des Nombres de Bordeaux, 18(3), 607–615. https://doi.org/10.5802/jtnb.561
@article{Klüners_2006, title={Asymptotics of number fields and the Cohen–Lenstra heuristics}, volume={18}, DOI={10.5802/jtnb.561}, number={3}, journal={Journal de Théorie des Nombres de Bordeaux}, publisher={Cellule MathDoc/CEDRAM}, author={Klüners, Jürgen}, year={2006}, pages={607–615} }
Klüners, Jürgen. “Asymptotics of Number Fields and the Cohen–Lenstra Heuristics.” Journal de Théorie Des Nombres de Bordeaux 18, no. 3 (2006): 607–15. https://doi.org/10.5802/jtnb.561.
J. Klüners, “Asymptotics of number fields and the Cohen–Lenstra heuristics,” Journal de Théorie des Nombres de Bordeaux, vol. 18, no. 3, pp. 607–615, 2006, doi: 10.5802/jtnb.561.
Klüners, Jürgen. “Asymptotics of Number Fields and the Cohen–Lenstra Heuristics.” Journal de Théorie Des Nombres de Bordeaux, vol. 18, no. 3, Cellule MathDoc/CEDRAM, 2006, pp. 607–15, doi:10.5802/jtnb.561.
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