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DENSITY OF IMAGINARY CUBIC FUNCTION FIELDS HAVING INFINITE HILBERT 3-CLASS FIELD TOWER

Jung, Hwanyup

  • Received : 2012.11.02
  • Accepted : 2012.12.11
  • Published : 2012.12.25

Abstract

In this paper we study the density of imaginary cubic function fields having the infinite Hilbert 3-class field tower.

Keywords

Density;Hilbert 3-class field tower;imaginary cubic function field

References

  1. J. Ahn and H. Jung, Hilbert 2-class field towers of imaginary quadratic function fields. J. Chungcheong Math. Soc. 23 (2010), no 4, 699-704.
  2. H. Jung, Density of class groups of imaginary ${\el}$-cyclic function fields. Finite fields and their applications 17 (2011), 286-293. https://doi.org/10.1016/j.ffa.2010.12.005
  3. H. Jung, Hilbert 3-class field towers of imaginary cubic function fields. submitted.
  4. M. Rosen, The Hilbert class field in function fields. Exposition. Math. 5 (1987), no. 4, 365-378.
  5. R. Schoof, Algebraic curves over $\mathbb{F}_{2}$ with many rational points. J. Number Theory 41 (1992), no. 1, 6-14. https://doi.org/10.1016/0022-314X(92)90079-5

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)