Pure fields of degree 9 with class number prime to 3
Annales de l'Institut Fourier, Volume 30 (1980) no. 2, p. 1-15

The main theorem gives necessary conditions and sufficient conditions for Q(n 9) to have class number prime to 3. These conditions involve only the rational prime factorization of n and congruences mod 27 of the prime factors of n. They give necessary and sufficient conditions for most n.

On détermine des conditions nécessaires et des conditions suffisantes pour que le nombre de classes de Q(n 9) soit premier à 3. Ces conditions n’utilisent que la factorisation en nombres premiers rationnels de n et des congruences mod 27 de ces facteurs premiers. Ils donnent des conditions nécessaires et suffisantes pour presque tout n.

@article{AIF_1980__30_2_1_0,
     author = {Walter, Colin D.},
     title = {Pure fields of degree 9 with class number prime to 3},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {30},
     number = {2},
     year = {1980},
     pages = {1-15},
     doi = {10.5802/aif.781},
     zbl = {0408.12009},
     mrnumber = {82b:12006},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1980__30_2_1_0}
}
Walter, Colin D. Pure fields of degree 9 with class number prime to 3. Annales de l'Institut Fourier, Volume 30 (1980) no. 2, pp. 1-15. doi : 10.5802/aif.781. http://www.numdam.org/item/AIF_1980__30_2_1_0/

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