On détermine des conditions nécessaires et des conditions suffisantes pour que le nombre de classes de
The main theorem gives necessary conditions and sufficient conditions for
@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}, pages = {1--15}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {30}, number = {2}, year = {1980}, doi = {10.5802/aif.781}, mrnumber = {82b:12006}, zbl = {0408.12009}, language = {en}, url = {https://www.numdam.org/articles/10.5802/aif.781/} }
TY - JOUR AU - Walter, Colin D. TI - Pure fields of degree 9 with class number prime to 3 JO - Annales de l'Institut Fourier PY - 1980 SP - 1 EP - 15 VL - 30 IS - 2 PB - Institut Fourier PP - Grenoble UR - https://www.numdam.org/articles/10.5802/aif.781/ DO - 10.5802/aif.781 LA - en ID - AIF_1980__30_2_1_0 ER -
Walter, Colin D. Pure fields of degree 9 with class number prime to 3. Annales de l'Institut Fourier, Tome 30 (1980) no. 2, pp. 1-15. doi : 10.5802/aif.781. https://www.numdam.org/articles/10.5802/aif.781/
[1] Remarks on principal factors in a relative cubic field, J. Number Theory, 3 (1971), 226-239. | MR | Zbl
and ,[2] Beziehungen zwischen Klassenzahlen von Teilkörpern eines galoisschen Körpers, Math. Nachr., 4 (1951), 158-174. | MR | Zbl
,[3] On the divisibility of the class number of Q(√9n) by 3, Mem. Fac. Sci., Kyushu Univ., A, 30 (1976), 299-311. | MR | Zbl
,[4] Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper, II, Physica-Verlag, Würzburg/Wien, 1970.
,[5] Pure cubic fields whose class numbers are multiples of three, J. Number Theory, 3 (1971), 7-12. | MR | Zbl
,[6] A note on class numbers of algebraic number fields, Abh. Math. Sem. Univ. Hamburg, 20 (1956), 257-258. | MR | Zbl
,[7] Class number relations in pure quintic fields, Symposia Mathematica, 15 (1975), 475-485. | MR | Zbl
,[8] A class number relation in Frobenius extensions of number fields, Mathematika, 24 (1977), 216-225. | MR | Zbl
,[9] Kuroda's class number relation, Acta Arithmetica, 35 (1979), 41-51. | MR | Zbl
,[10] The ambiguous class group and the genus group of certain non-normal extensions, Mathematika, 26 (1979), 113-124. | MR | Zbl
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