DOI QR코드

DOI QR Code

DETERMINATION OF ALL SUBFIELDS OF CYCLOTOMIC FUNCTION FIELDS WITH GENUS ONE

  • JUNG, HWAN-YUP (Department of Mathematics Education Chungbuk National University) ;
  • AHN, JAE-HYUN (Department of Mathematics Chungnam National University)
  • 발행 : 2005.04.01

초록

In this paper we determine all subfields with genus one of cyclotomic function fields over rational function fields explicitly.

키워드

참고문헌

  1. B. Angles, On Hilbert class field towers of global function fields, in 'Drinfeld modules, modular schemes and applications', 261-271, World Sci. Publishing, River Edge, NJ, 1997
  2. R. Auer, Ray class fields of global function fields with many rational places, Dissertation at the University of Oldenburg, 1999
  3. H. L. Claasen, The group of units in GF(q)[x]/(a(x)), Nederl. Akad. Wetensch. Proc. Ser. A 80=Indag. Math. 39 (1977), no. 4, 245-255.
  4. R. Clement, The genus field of an algebraic function field, J. Number Theory 40 (1992), no. 3, 359-375 https://doi.org/10.1016/0022-314X(92)90007-C
  5. H. Jung, and J. Ahn, Divisor class number one problem for abelian extensions over rational function fields, to appear in J. of Algebra
  6. M. Kida, and N. Murabayashi, Cyclotomic functions fields and divisor class number one, Tokyo J. Math. 14 (1991), no. 1, 45-56 https://doi.org/10.3836/tjm/1270130486
  7. M. Rosen, Number theory in function fields, Graduate Texts in Mathematics, Springer-Verlag, New York, 210 (2002)
  8. H. Stichtenoth, Algebraic function fields and codes, Universitext, Springer Verlag, 1993
  9. L. Washington, Introduction to cyclotomic fields, Graduate Texts in Mathematics, Springer-Verlag, New York, 83 (1997)