Skip to main content
Log in

On the holomorphic differential forms of the Siegel modular variety

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. A. N. Andrianov andG. N. Maloletkin, Behaviour of theta series of degreen under modular substitutions. Math. USSR-Izv.9, 227–241 (1975).

    Google Scholar 

  2. S. Böcherer, über die Fourier-Jacobi-Entwicklung Siegelscher Eisensteinreihen II. Math. Z.189, 81–110 (1985).

    Google Scholar 

  3. E. Freitag, Der Körper der Siegelschen Modulfunktionen. Abh. Math. Sem. Univ. Hamburg47, 25–41 (1975).

    Google Scholar 

  4. E. Freitag, Thetareihen mit harmonischen Koeffizienten zur Siegelschen Modulgruppe. Math. Ann.254, 27–51 (1980).

    Google Scholar 

  5. E. Freitag undK. Pommerening, Regular Differentialformen des Körpers der Siegelschen Modulfunktionen. J. Reine Angew. Math.331, 207–220 (1982).

    Google Scholar 

  6. J. I. Igusa, On the graded ring of theta constants. Amer. J. Math.86, 219–246 (1964).

    Google Scholar 

  7. J. I.Igusa, Theta functions. Grundlehren Math. Wiss.194, Berlin-Heidelberg-New York 1972.

  8. M. Kashiwara andM. Vergne, On the Segal-Shale-Weil representations and harmonic poly-nomials. Invent. Math.44, 1–47 (1978).

    Google Scholar 

  9. D.Mumford, Tata Lectures on Theta I. Progress in Math.28, Boston-Basel-Stuttgart 1983.

  10. R. Salvati-Manni, Holomorphic differential forms of degreeN−1 invariant under γ g . J. Reine Angew. Math.382, 74–84 (1987).

    Google Scholar 

  11. M.Stillman, Construction of holomorphic differential form on the moduli space of abelian varieties. Ph.D. Thesis, Harvard University 1983.

  12. R. Weissauer, Vektorwertige Siegelsche Modulformen Kleinen Gewichtes. J. Reine Angew. Math.343, 184–202 (1983).

    Google Scholar 

  13. R.Weissauer, Stabile Modulformen und Eisensteinreihen. LNM1219, Berlin-Heidelberg-New York 1986.

  14. R. Weissauer, Divisors of the Siegel modular variety. LNM1240, 304–324, Berlin-Heidelberg-New York 1987.

    Google Scholar 

  15. R. Weissauer, Stable Modular Forms-The Selberg trace formula and related topics. Proc. AMS-IMS-SIAM, Joint Summer Res. Conf. Contemp. Math.53, 535–542 (1986).

    Google Scholar 

  16. E. Freitag, Die Wirkung von Heckeoperatoren auf Thetareihen mit harmonischen Koeffizien-ten. Math. Ann.258, 419–440 (1982).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Manni, R.S. On the holomorphic differential forms of the Siegel modular variety. Arch. Math 53, 363–372 (1989). https://doi.org/10.1007/BF01195216

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01195216

Keywords

Navigation