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Elliptic Units in Function Fields

  • David R. Hayes
Part of the Progress in Mathematics book series (PM, volume 26)

Abstract

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.

Keywords

Prime Ideal Galois Group Class Number Positive Element Class Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [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
  2. [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
  3. [GR]
    S. Galovich and M. Rosen. “Units and Class Groups in Cyclotomic Function Fields,” to appear in the J. of Number Theory. Google Scholar
  4. [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
  5. [H2]
    D. Hayes. “Analytic Class Number Formulas in Global Function Fields,” Inventiones Math. 65 (1981), 49–69.CrossRefGoogle Scholar
  6. [R]
    G. Robert. “Unites el1iptiques,” Bull. Soc. Math. France, Mem. No. 36 (1973).Google Scholar
  7. [Ros]
    M. Rosen. “S-Units and S-Class Group in Algebraic Function Fields,” J. Algebra 26 (1973), 98–108.CrossRefGoogle Scholar
  8. [S]
    W. Sinnott. “On the Stiekel berger Ideal and Circular Units of a Cyclotomic Field,” Ann. of Math. 108 (1978), 107–134.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1982

Authors and Affiliations

  • David R. Hayes
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of MassachusettsAmherstUSA

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