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HILBERT 2-CLASS FIELD TOWERS OF IMAGINARY QUADRATIC FUNCTION FIELDS

  • Jung, Hwanyup (Department of Mathematics Education Chungbuk National University)
  • Received : 2012.07.07
  • Published : 2013.05.31

Abstract

In this paper we study the infiniteness of Hilbert 2-class field towers of imaginary quadratic function fields over $\mathbb{F}_q(T)$, where $q$ is a power of an odd prime number.

Keywords

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

References

  1. S. Bae, S. Hu, and H. Jung, The generalized Redei matrix for function fields, Finite Fields Appl. 18 (2012), no. 4, 760-780. https://doi.org/10.1016/j.ffa.2012.01.004
  2. F. Gerth, Quadratic fields with infinite Hilbert 2-class field towers, Acta. Arith. 106 (2003), no. 2, 151-158. https://doi.org/10.4064/aa106-2-5
  3. F. Hajir, On a theorem of Koch, Pacific J. Math. 176 (1996), no. 1, 15-18. https://doi.org/10.2140/pjm.1996.176.15
  4. F. Hajir, Correction to "On a theorem of Koch", Pacific J. Math. 196 (2000), no. 2, 507-508.
  5. H. Koch, Uber den 2-Klassenkorperturm eines quadratischen Zahlkorpers, J. Reine Angew. Math. 214/215 (1964), 201-206.
  6. J. Martinet, Tours de corps de classes et estimations de discriminants, Invent. Math. 44 (1978), no. 1, 65-73. https://doi.org/10.1007/BF01389902
  7. M. Rosen, The Hilbert class field in function fields, Exposition. Math. 5 (1987), no. 4, 365-378.
  8. M. Rosen, Number Theory in Function Fields, Graduate Texts in Mathematics, 210. Springer-Verlag, New York, 2002.
  9. 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
  10. C. Wittmann, Densities for 4-ranks of quadratic function fields, J. Number Theory 129 (2009), no. 10, 2635-2645. https://doi.org/10.1016/j.jnt.2009.03.004