Divisibility of class numbers of non-normal totally real cubic number fields
Lee, Jungyun
Proc. Japan Acad. Ser. A Math. Sci., Tome 86 (2010) no. 1, p. 38-40 / Harvested from Project Euclid
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In this paper, we consider a family of cubic fields $\{K_m\}_{m\geq4}$ associated to the irreducible cubic polynomials $P_m(x)=x^3-mx^2-(m+1)x-1,\,\,\,(m\geq4).$ We prove that there are infinitely many $\{K_m\}_{m\geq4}$'s whose class numbers are divisible by a given integer n. From this, we find that there are infinitely many non-normal totally real cubic fields with class number divisible by any given integer n.
Publié le : 2010-02-15
Classification:  Class number,  totally real cubic fields,  11R29,  11R80 
@article{1265033220,
     author = {Lee, Jungyun},
     title = {Divisibility of class numbers of non-normal totally real cubic number fields},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {86},
     number = {1},
     year = {2010},
     pages = { 38-40},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1265033220}
}

Lee, Jungyun. Divisibility of class numbers of non-normal totally real cubic number fields. Proc. Japan Acad. Ser. A Math. Sci., Tome 86 (2010) no. 1, pp.  38-40. http://gdmltest.u-ga.fr/item/1265033220/