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Index Formulas for Ramified Elliptic Units

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Compositio Mathematica

Abstract

We compute the index of certains groups of elliptic units. These groups are the analoguousof Sinnott's groups of circular units.

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References

  1. Belliard, J.–R. and Oukhaba, H.: Sur la torsion de la distribution ordinaire universelle attachée à un corps de nombres, Manuscripta Math. 106 (2001), 117–130.

    Google Scholar 

  2. Galovich, S. and Rosen, M.: Units and class group in cyclotomic function fields, J. Number Theory 14 (1982), 156–184.

    Google Scholar 

  3. Gross, B. and Rosen, M.: Fourier series and the special values of L–functions, Adv. in Math. 69 (1988), 1–31.

    Google Scholar 

  4. Hajir, F. and Villegas, F. R.: Explicit elliptic units 1, Duke Math. J. 90 (1997), 495–521.

    Google Scholar 

  5. Kubert, D. and Lang, S.: Modular Units, Lecture Notes in Math 244, Springer, New York, 1981.

    Google Scholar 

  6. Lang, S.: Elliptic Functions, Addison–Wesley, Reading, Mass., 1973.

    Google Scholar 

  7. Ramachandra, K.:Some applications of Kronecker limit formulas, Ann. of Math 80 (1964), 104–148.

    Google Scholar 

  8. Robert, G.: Unités elliptiques, Bull. Soc. Math. France, Suppl. 36 Deécembre 1973.

  9. Robert, G.: Concernant la relation de distribution satisfaite par la fonction ϕ associée à un rè seau complexe, Invent. Math. 100 (1990), 231–257.

    Google Scholar 

  10. Robert, G.: La racine 12–iè me canonique de Δ(L)[{ie22–1}:L]/Δ({ie22–2}), In:Sè minaire de thè orie des nombres, Paris, 1989–90.

    Google Scholar 

  11. Rubin, K.: The ‘main conjectures’ of Iwasawa theory for imaginary quadratic fields, Invent. Math. 103 (1991), 25–68.

    Google Scholar 

  12. Schertz, R.: Niedere Potenzen elliptischer Einheiten, In: Proc. Int. Conf. Class Numbers and Fundamental Units of Algebraic Number Fields, 24–28 June, Katata, Japan, 1986.

  13. Sinnott, W.: On the Stickelberger ideal and the circular units of a cyclotomic field, Ann. of Math. 108 (1978), 107–134.

    Google Scholar 

  14. Sinnott, W.: On the Stichelberger ideal and the circular units of an Abelian field, Invent. Math. 62 (1980), 181–234.

    Google Scholar 

  15. Stark, H. M.: L–functions at s = 1. IV. First derivatives at s 0, Adv. in Math. 35 (1980), 197–235.

    Google Scholar 

  16. Tate, J.: Les conjectures de Stark sur les fonctions d'Artin en s = 0, In: Cours à Orsay, Notes de D. Bernardi et N. Schappacher, Progr. in Math. 47, Birkhaü ser, Basel, 1984.

    Google Scholar 

  17. Yin, L.: Index–class number formulas over global function fields, Compositio Math. 109 (1997), 49–66.

    Google Scholar 

  18. _ Yin, L.: On the index of cyclotomic units in characteristic p and its applications, J. Number Theory 63 (1997), 302–324.

    Google Scholar 

  19. _ Yin, L.: Distributions on global fields, J. Number Theory 80 (2000), 154–167.

    Google Scholar 

Download references

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Authors and Affiliations

  1. Laboratoire de Mathématiques CNRS UMR 6623, Université de Franche-Comte, 16 route de Gray, 25030, Besanc¸on Cedex, France

    Hassan Oukhaba

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  1. Hassan Oukhaba
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Oukhaba, H. Index Formulas for Ramified Elliptic Units. Compositio Mathematica 137, 1–22 (2003). https://doi.org/10.1023/A:1023667807218

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