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REAL QUADRATIC FUNCTION FIELDS OF MINIMAL TYPE

  • Byeon, Dongho (Department of Mathematics Seoul National University) ;
  • Keem, Jiae (Department of Mathematics Seoul National University) ;
  • Lee, Sangyoon (Department of Mathematics Seoul National University)
  • Received : 2013.01.09
  • Published : 2013.10.31

Abstract

In this paper, we will introduce the notion of the real quadratic function fields of minimal type, which is a function field analogue to Kawamoto and Tomita's notion of real quadratic fields of minimal type. As number field cases, we will show that there are exactly 6 real quadratic function fields of class number one that are not of minimal type.

Keywords

References

  1. D. Byeon and S. Lee, A note on units of real quadratic fields, Bull. Korean Math. Soc. 49 (2012), no. 4, 767-774. https://doi.org/10.4134/BKMS.2012.49.4.767
  2. K. Feng and W. Hu, On real quadratic function fields of Chowla type with ideal class number one, Proc. Amer. Math. Soc. 127 (1999), no. 5, 1301-1307. https://doi.org/10.1090/S0002-9939-99-05004-2
  3. K. Feng and S. Sun, On class number of quadratic fields, Proceeding of First International Symposium on Algebraic Structures and Number Theory (1988, Hong Kong), Edited by S. P. Lam and K. P. Shum, World Scientific, (1990), 88-133.
  4. R. Hashimoto, Ankeny-Artin-Chowla conjecture and continued fraction, J. Number Theory 90 (2001), no. 1, 143-153. https://doi.org/10.1006/jnth.2001.2652
  5. F. Kawamoto and K. Tomita, Continued fractions and certain real quadratic fields of minimal type, J. Math. Soc. Japan 60 (2008), no. 3, 865-903. https://doi.org/10.2969/jmsj/06030865
  6. M. Madan and C. Queen, Algebraic function fields of class number one, Acta Arith. 20 (1972), 423-432. https://doi.org/10.4064/aa-20-4-423-432
  7. J. Mc Laughlin, Multi-variable polynomial solutions to Pell's equation and fundamental units in real quadratic fields Pacific J. Math. 210 (2003), no. 2, 335-349. https://doi.org/10.2140/pjm.2003.210.335
  8. A. Stein, Introduction to continued fraction expansion in real quadratic function fields, Preprint.