Eine Klassenzahlformel für singuläre Moduln der Picardschen Modulgruppen

Jan Feustel

Compositio Mathematica (1990)

  • Volume: 76, Issue: 1-2, page 87-100
  • ISSN: 0010-437X

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Feustel, Jan. "Eine Klassenzahlformel für singuläre Moduln der Picardschen Modulgruppen." Compositio Mathematica 76.1-2 (1990): 87-100. <http://eudml.org/doc/90057>.

@article{Feustel1990,
author = {Feustel, Jan},
journal = {Compositio Mathematica},
keywords = {elliptic modular group; Picard modular group; imaginary quadratic field; K-singular moduli; Hilbert modular group; jacobian; class-numbers of CM-extension},
language = {ger},
number = {1-2},
pages = {87-100},
publisher = {Kluwer Academic Publishers},
title = {Eine Klassenzahlformel für singuläre Moduln der Picardschen Modulgruppen},
url = {http://eudml.org/doc/90057},
volume = {76},
year = {1990},
}

TY - JOUR
AU - Feustel, Jan
TI - Eine Klassenzahlformel für singuläre Moduln der Picardschen Modulgruppen
JO - Compositio Mathematica
PY - 1990
PB - Kluwer Academic Publishers
VL - 76
IS - 1-2
SP - 87
EP - 100
LA - ger
KW - elliptic modular group; Picard modular group; imaginary quadratic field; K-singular moduli; Hilbert modular group; jacobian; class-numbers of CM-extension
UR - http://eudml.org/doc/90057
ER -

References

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  1. [0] Feustel, J.-M., Holzapfel, R.-P.: Symmetry points and Chern invariants of Picard modular surfaces, Math. Nachr.111 (1983), S.7-40. Zbl0528.14015MR725771
  2. [1] Feustel, J.-M.: Representation of Picard modular forms by theta constants, Rev. Roumaine Math. Pures Appl.33 (1988), S.275-281. Zbl0662.10020MR950127
  3. [1a] Feustel, J.-M.: Arithmetik und Geometrie Picardscher Modulflächen, Dissertation B, Akademie der Wissenschaften der DDR, Karl-Weierstrass-Institut für Mathematik (1987). 
  4. [2] Hasse, H.: Zahlentheorie,Akademie Verlag, Berlin (1963). Zbl1038.11500MR153659
  5. [2a] Hasse, H.: Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper, Teil I, B. G. Teubner, Leipzig/Berlin (1930). JFM56.0165.01
  6. [3] Hecke, E.: Zur Theorie der Modulfunktionen von 2 Variablen und ihre Anwendung auf die Zahlentheorie, Math. Annalen71, (1912), S.1-37. Zbl42.0457.01JFM42.0457.01
  7. [4] Holzapfel, R.-P.: Geometry and arithmetic around Euler partial differential equations, Kluwer Academic Publishers, Dordrecht, Holland, (1986). Zbl0595.14016MR849778
  8. [5] Holzapfel, R.-P.: An arithmetic uniformization for arithmetic points of the plane by singular moduli, J. Ramanujan Math. Soc.3(1), (1988), S.35-62. Zbl0692.10024MR975836
  9. [6] Lang, S.: Complex multiplication, New York, Berlin, Heidelberg, Tokyo, Springer (1983). Zbl0536.14029MR713612
  10. [7] Picard, E.: Sur des fonctions de deux variables independentes analogues aux fonctions modulaires, Acta Mathematica2 (1983), S.114-135. JFM15.0432.01
  11. [8] Picard, E.: Sur les formes quadratiques rerneires indefinies et sur les fonctions hyperfuchsiennes, Acta Mathematica5 (1884), S.121-182. JFM16.0385.01
  12. [9] Reiner, I.: A survey of integral representation theory, Bulletin of the American Mathematical Society, Vol. 76, No. 2, (1970), S.159-227. Zbl0194.04701MR254092
  13. [10] Shiga, H.: On the representation of Picard modular function by Θ constants I-II, Publ. RIMS, Kyoto Univ., 24 (1988), S. 311-360. Zbl0678.10020
  14. [11] Shiga, H.: On the construction of algebraic numbers as special values of the Picard modular function, Preprint, Chiba University. 
  15. [12] Shimura, G.: On analytic families of polarized Abelian varieties and automorphic functions, Annals of Mathematic, 78 (1963) No. 1, S. 149-192. Zbl0142.05402MR156001
  16. [13] Shimura, G.: Arithmetic of unitary groups, Annals of Mathematic, 79 (1964), S. 369-409. Zbl0144.29504MR158882
  17. [14] Scharlau, W.: Quadratic and hermitianforms, Springer, Berlin, Heidelberg, New York, Tokyo, (1985). Zbl0584.10010

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