Quadratic function fields whose class numbers are not divisible by three

Humio Ichimura

Acta Arithmetica (1999)

  • Volume: 91, Issue: 2, page 181-190
  • ISSN: 0065-1036

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Humio Ichimura. "Quadratic function fields whose class numbers are not divisible by three." Acta Arithmetica 91.2 (1999): 181-190. <http://eudml.org/doc/207348>.

@article{HumioIchimura1999,
author = {Humio Ichimura},
journal = {Acta Arithmetica},
keywords = {quadratic function fields; divisor class number},
language = {eng},
number = {2},
pages = {181-190},
title = {Quadratic function fields whose class numbers are not divisible by three},
url = {http://eudml.org/doc/207348},
volume = {91},
year = {1999},
}

TY - JOUR
AU - Humio Ichimura
TI - Quadratic function fields whose class numbers are not divisible by three
JO - Acta Arithmetica
PY - 1999
VL - 91
IS - 2
SP - 181
EP - 190
LA - eng
KW - quadratic function fields; divisor class number
UR - http://eudml.org/doc/207348
ER -

References

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  1. [1] E. Artin, Quadratische Körper im Gebiet der höheren Kongruenzen I und II, Math. Z. 19 (1923), 153-246. Zbl50.0107.01
  2. [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. 
  3. [3] G. Cornell, Relative genus theory and the class group of l-extensions, Trans. Amer. Math. Soc. 277 (1983), 321-429. Zbl0514.12012
  4. [4] B. Datskovsky and D. J. Wright, Density of discriminants of cubic extensions, J. Reine Angew. Math. 386 (1988), 116-138. Zbl0632.12007
  5. [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. Zbl0212.08101
  6. [6] C. Friesen, Class number divisibility in real quadratic function fields, Canad. Math. Bull. 35 (1992), 361-370. Zbl0727.11045
  7. [7] M. Hall, The Theory of Groups, Macmillan, New York, 1959. 
  8. [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. 
  9. [9] K. Horie, A note on basic Iwasawa λ-invariants of imaginary quadratic fields, Invent. Math. 88 (1987), 31-38. 
  10. [10] H. Ichimura, On the class groups of pure function fields, Proc. Japan Acad. 64 (1988), 170-173; corrigendum, ibid. 75 (1999), 22. Zbl0664.12006
  11. [11] K. Iwasawa, A note on class numbers of algebraic number fields, Abh. Math. Sem. Univ. Hamburg 20 (1956), 257-258. Zbl0074.03002
  12. [12] I. Kimura, On class numbers of quadratic extensions over function fields, Manuscripta Math. 97 (1998), 81-91. Zbl0911.11053
  13. [13] T. Nagell, Über die Klassenzahl imaginär-quadratischer Zahlkörper, Abh. Math. Sem. Univ. Hamburg 1 (1922), 140-150. Zbl48.0170.03
  14. [14] P. Roquette and H. Zassenhaus, A class rank estimate for algebraic number fields, J. London Math. Soc. 44 (1969), 31-38. Zbl0169.38001
  15. [15] M. Rosen, The Hilbert class fields in function fields, Exposition. Math. 5 (1987), 365-378. Zbl0632.12017
  16. [16] D. Shanks, The simplest cubic fields, Math. Comp. 28 (1974), 1137-1157. Zbl0307.12005
  17. [17] Y. Yamamoto, On unramified Galois extensions of quadratic number fields, Osaka J. Math. 7 (1970), 57-76. Zbl0222.12003

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