@article{bwmeta1.element.bwnjournal-article-aav91i2p181bwm,
author = {Humio Ichimura},
title = {Quadratic function fields whose class numbers are not divisible by three},
journal = {Acta Arithmetica},
volume = {89},
year = {1999},
pages = {181-190},
zbl = {0938.11057},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav91i2p181bwm}
}
Humio Ichimura. Quadratic function fields whose class numbers are not divisible by three. Acta Arithmetica, Tome 89 (1999) pp. 181-190. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav91i2p181bwm/
[000] [1] E. Artin, Quadratische Körper im Gebiet der höheren Kongruenzen I und II, Math. Z. 19 (1923), 153-246. | Zbl 50.0107.01
[001] [2] G. Cornell, Abhyankar's lemma and the class group, in: Number Theory, Carbondale, 1979, M. Nathanson (ed.), Lecture Notes in Math. 751, Springer, New York, 1981, 82-88.
[002] [3] G. Cornell, Relative genus theory and the class group of l-extensions, Trans. Amer. Math. Soc. 277 (1983), 321-429. | Zbl 0514.12012
[003] [4] B. Datskovsky and D. J. Wright, Density of discriminants of cubic extensions, J. Reine Angew. Math. 386 (1988), 116-138. | Zbl 0632.12007
[004] [5] H. Davenport and H. Heilbronn, On the density of discriminants of cubic fields II, Proc. Roy. Soc. London Ser. A 322 (1971), 405-420. | Zbl 0212.08101
[005] [6] C. Friesen, Class number divisibility in real quadratic function fields, Canad. Math. Bull. 35 (1992), 361-370. | Zbl 0727.11045
[006] [7] M. Hall, The Theory of Groups, Macmillan, New York, 1959.
[007] [8] P. Hartung, Proof of the existence of infinitely many imaginary quadratic fields whose class numbers are not divisible by three, J. Number Theory 6 (1976), 276-278.
[008] [9] K. Horie, A note on basic Iwasawa λ-invariants of imaginary quadratic fields, Invent. Math. 88 (1987), 31-38.
[009] [10] H. Ichimura, On the class groups of pure function fields, Proc. Japan Acad. 64 (1988), 170-173; corrigendum, ibid. 75 (1999), 22. | Zbl 0664.12006
[010] [11] K. Iwasawa, A note on class numbers of algebraic number fields, Abh. Math. Sem. Univ. Hamburg 20 (1956), 257-258. | Zbl 0074.03002
[011] [12] I. Kimura, On class numbers of quadratic extensions over function fields, Manuscripta Math. 97 (1998), 81-91. | Zbl 0911.11053
[012] [13] T. Nagell, Über die Klassenzahl imaginär-quadratischer Zahlkörper, Abh. Math. Sem. Univ. Hamburg 1 (1922), 140-150. | Zbl 48.0170.03
[013] [14] P. Roquette and H. Zassenhaus, A class rank estimate for algebraic number fields, J. London Math. Soc. 44 (1969), 31-38. | Zbl 0169.38001
[014] [15] M. Rosen, The Hilbert class fields in function fields, Exposition. Math. 5 (1987), 365-378. | Zbl 0632.12017
[015] [16] D. Shanks, The simplest cubic fields, Math. Comp. 28 (1974), 1137-1157. | Zbl 0307.12005
[016] [17] Y. Yamamoto, On unramified Galois extensions of quadratic number fields, Osaka J. Math. 7 (1970), 57-76. | Zbl 0222.12003