DOI QR코드

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KUCERA GROUP OF CIRCULAR UNITS IN FUNCTION FIELDS

  • Ahn, Jae-Hyun ;
  • Jung, Hwan-Yup
  • 발행 : 2007.05.31

초록

Let $\mathbb{A}=\mathbb{F}_q$[T] be the polynomial ring over a finite field $\mathbb{F}_q$[T] and K=$\mathbb{F}_q$(T) its field of fractions. Let ${\ell}$ be a fixed prime divisor of q-1. Let J be a finite set of monic irreducible polynomials $P{\in}{\mathbb{A}}$ with deg $P{\equiv}0$ (mod ${\ell})$. In this paper we define the group $C_K$ of circular units in K=k$(\{\sqrt[{\ell}]P\;:\;P{\in}J\})$ in the sense of Kucera [4] and compute the index of $C_K$ in the full unit group $O^*_K$.

키워드

Kucera group;circular units;function fields

참고문헌

  1. B. Angles, On Hilbert class field towers of global function fields, Drinfeld modules, modular schemes and applications (Alden-Biesen, 1996), 261-271, World Sci. Publ., River Edge, NJ, 1997
  2. J. Ahn, S. Bae, and H. Jung, Cyclotomic units and Stickelberger ideals of global function fields, Trans. Amer. Math. Soc. 355 (2003), no. 5, 1803-1818 https://doi.org/10.1090/S0002-9947-03-03245-8
  3. J. Ahn and H. Jung, Cyclotomic units and divisibility of the class number of function fields, J. Korean Math. Soc. 39 (2002), no. 5, 765-773 https://doi.org/10.4134/JKMS.2002.39.5.765
  4. W. Sinnott, On the Stickelberger ideal and the circular units of an abelian field, Invent. Math. 62 (1980/81), no. 2, 181-234
  5. M. Rosen, Number theory in function fields, Graduate Texts in Mathematics, 210. Springer-Verlag, New York, 2002
  6. R. Kucera, On the Stickelberger ideal and circular units of a compositum of quadratic fields, J. Number Theory 56 (1996), no. 1, 139-166 https://doi.org/10.1006/jnth.1996.0008