대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제27권2호
  • /
  • Pages.223-231
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  • 2012
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  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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4-RANKS OF CLASS GROUPS OF QUADRATIC EXTENSIONS OF CERTAIN QUADRATIC FUNCTION FIELDS

  • 투고 : 2010.11.05
  • 발행 : 2012.04.30
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초록

We obtain some density results for the 4-ranks of class groups of quadratic extensions of quadratic function fields analogous to those results of F. Gerth in the classical case.

키워드

참고문헌

  1. S. Bae and H. Jung, $\ell$-ranks of class groups of function fields, submitted.
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  3. F. Gerth, The 4-class ranks of quadratic fields, Invent. Math. 77 (1984), no. 3, 489-515. https://doi.org/10.1007/BF01388835
  4. F. Gerth, Limit probabilities for coranks of matrices over GF(q), Linear and Multilinear Algebra 19 (1986), no. 1, 79-93. https://doi.org/10.1080/03081088608817706
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  6. F. Gerth, The 4-class ranks of quadratic extensions of certain imaginary quadratic fields, Illinois J. Math. 33 (1989), no. 1, 132-142.
  7. F. Halter-Koch, Ein Satz uber die Geschlechter relativ-zyklischer Zahlkorper von Primzahlgrad und seine Anwendung auf biquadratische-bizyklische Korper, J. Number Theory 4 (1972), 144-156. https://doi.org/10.1016/0022-314X(72)90060-1
  8. C. Wittmann, $\ell$-class groups of cyclic function fields of degree $\ell$, Finite Fields Appl. 13 (2007), no. 2, 327-347. https://doi.org/10.1016/j.ffa.2005.09.001