Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

DENSITIES FOR 4-RANKS OF REAL QUADRATIC FUNCTION FIELDS

  • Jung, Hwanyup (Department of Mathematics Education Chungbuk National University)
  • Received : 2014.05.27
  • Accepted : 2014.10.06
  • Published : 2014.11.15
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we study of densities of the 4-rank of narrow ideal class groups of real quadratic function fields over the rational function field $\mathbb{F}_q(T)$ when $q{\equiv}3$ mod 4.

Keywords

Acknowledgement

Supported by : Chungbuk National University

References

  1. S. Bae and H. Jung, $\ell$-ranks of class groups of function fields, J. Korean Math. Soc. 49 (2012), no. 1, 49-67. https://doi.org/10.4134/JKMS.2012.49.1.049
  2. F. Gerth, III, The 4-class ranks of quadratic fields, Invent. Math. 77 (1984), no. 3, 489-515. https://doi.org/10.1007/BF01388835
  3. H. Jung, Density of class groups of imaginary $\ell$-cyclic function fields, Finite Fields Appl. 17 (2011), no. 3, 286-293. https://doi.org/10.1016/j.ffa.2010.12.005
  4. M. Rosen, Number theory in function fields, Graduate Texts in Mathematics 210, Springer-Verlag, New York, 2002, xii+358.
  5. C. Wittmann, l-class groups of cyclic function fields of degree l, Finite Fields Appl. 13 (2007), no. 2, 327-347. https://doi.org/10.1016/j.ffa.2005.09.001
  6. C. Wittmann, Densities for 4-class ranks of quadratic function fields, J. Number Theory 129 (2009), no. 10, 2635-2645. https://doi.org/10.1016/j.jnt.2009.03.004