Elliptic Units in Function Fields
In [R], Robert uses modular functions to construct units in the class fields H of an imaginary quadratic number field F. In case H/F has prime power conductor, he computes the index of these “elliptic units” in the full unit group of H and finds that, up to trivial factors, the index is the class number of H. He therefore refers to his results on indices as class number formulas.
KeywordsPrime Ideal Galois Group Class Number Positive Element Class Field
Unable to display preview. Download preview PDF.
- [D]V.G. Drinfeld. “Elliptic Modules” (Russian), Math Sbornik 94 (1974), 594–627 (Engl ish translation, Math. USSR Sbomik 23(1974), no. 4.)Google Scholar
- [B]B. Gross. “The Annihilation of Divisor Classes in Abelian Exten- sions of the Rational Function Field,” Seminaire de Theorie des Nombres, (Bordeaux), (1980–81), expose no. 3.Google Scholar
- [GR]S. Galovich and M. Rosen. “Units and Class Groups in Cyclotomic Function Fields,” to appear in the J. of Number Theory. Google Scholar
- [Hl]D. Hayes. “Explicit Class Field Theory in Global Function Fields,” Studies in Algebra and Number Theory, G.-C. Rota (ed.), Academic Press, New York, 1979.Google Scholar
- [R]G. Robert. “Unites el1iptiques,” Bull. Soc. Math. France, Mem. No. 36 (1973).Google Scholar