Skip to main content
SpringerLink
Log in

Theta functions and Siegel-Jacobi forms

  • Published:
Acta Mathematica

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  • [B1]Berndt, R., Zur Arithmetik der elliptischen Funktionenkörper höherer Stufe.J. Reine Angew. Math., 326 (1981), 79–94.

    MATH  MathSciNet  Google Scholar 

  • [B2] —, Meromorphe Funktionen auf Mumfords Kompaktifizierung der universellen elliptischen Kurve.J. Reine Angew. Math., 326 (1981), 95–101.

    MATH  MathSciNet  Google Scholar 

  • [Ch]Chai, Ch.-L.,Compactification of Siegel Moduli Schemes. London Math Soc. Lecture Note Ser., 107. Cambridge Univ. Press, Cambridge-New York, 1985.

    MATH  Google Scholar 

  • [El]Elstrodt, J., Eine Charakterisierung der Eisenstein-Reihe zur Siegelschen Modulgruppe.Math. Ann., 268 (1984), 473–474.

    Article  MATH  MathSciNet  Google Scholar 

  • [EZ]Eichler, M. &Zagier, D.,The Theory of Jacobi Forms. Progr. Math., 55. Birkhäuser, Boston, MA, 1985.

    MATH  Google Scholar 

  • [Fr]Freitag, E.,Siegelsche Modulfunktionen. Grundlehren Math. Wiss., 254. Springer-Verlag, New York-Berlin, 1983.

    MATH  Google Scholar 

  • [GN1]Geemen, B. van & Nygaard, N. O. L-functions of some Siegel modular 3-folds. Preprint 546, Utrecht, 1988.

  • [GN2]Geemen, B. van & Nygaard, N. O., On the geometry and arithmetic of some Siegel modular threefolds. Preprint, 1991.

  • [Ha]Hartshorne, R.,Algebraic Geometry. Graduate Texts in Math., 52. Springer-Verlag, New York-Berlin, 1977.

    MATH  Google Scholar 

  • [Ig1]Igusa, J., On the graded ring of theta-constants.Amer. J. Math., 86 (1964), 219–246.

    MATH  MathSciNet  Google Scholar 

  • [Ig2] —, On the graded ring of theta constants, II.Amer. J. Math., 88 (1966), 221–236.

    MATH  MathSciNet  Google Scholar 

  • [Ig3] —,Theta Functions. Grundlehren Math. Wiss., 194, Springer-Verlag, New York-Berlin, 1972.

    MATH  Google Scholar 

  • [Ig4] —, On the varieties associated with the ring of thetanullwerte.Amer. J. Math., 103 (1981), 377–398.

    MATH  MathSciNet  Google Scholar 

  • [K1]Kramer, J., The theory of Siegel-Jacobi forms. Habilitationsschrift, Zürich, 1992.

  • [K2] —, A geometric approach to the theory of Jacobi forms.Compositio Math., 79 (1991), 1–19.

    MATH  MathSciNet  Google Scholar 

  • [Koe]Koecher, M., Zur Theorie der Modulformenn-ten Grades, I.Math. Z., 59 (1954), 399–416.

    Article  MATH  MathSciNet  Google Scholar 

  • [Kr]Krazer, A.,Lehrbuch der Thetafunktionen. Teubner, Leipzig, 1903.

    MATH  Google Scholar 

  • [Me]Mennicke, J. L., Zur Theorie der Siegelschen Modulgruppe.Math. Ann., 159 (1965), 115–129.

    Article  MATH  MathSciNet  Google Scholar 

  • [Mu]Mumford, D.,Tata Lectures on Theta, Vols. 1–3., Progr. Math., 28, 43, 97. Birkhäuser, Boston, MA, 1983, 1984, 1991.

    MATH  Google Scholar 

  • [R1]Runge, B., On Siegel modular forms, part I.J. Reine Angew. Math., 436 (1993) 57–85.

    MATH  MathSciNet  Google Scholar 

  • [R2] — On Siegel modular forms, part II,Nagoya Math. J., 138 (1995), 179–197.

    MATH  MathSciNet  Google Scholar 

  • [R3]Runge, B. Codes and Siegel modular forms. To appear inDiscrete Math.

  • [R4] —, The Schottky ideal, inAbelian Varieties, Proceedings of the International Conference, Eggloffstein, 1993, pp. 251–272. Walter de Gruyter, Berlin-New York, 1995.

    Google Scholar 

  • [R5]Runge, B. Level-two-structures and hyperelliptic curves. Preprint, 1993.

  • [R6]Runge, B. Modulräume in Geschlecht 3. Habilitationsschrift, Mannheim 1993.

  • [S1]Stanley, R. P., Hilbert functions of graded algebras.Adv. in Math., 28 (1978), 57–83.

    Article  MATH  MathSciNet  Google Scholar 

  • [S2] —, Invariants of finite groups and their applications to combinatorics.Bull. Amer. Math Soc. (N. S.), 1 (1979), 475–511.

    Article  MATH  MathSciNet  Google Scholar 

  • [Sh]Shioda, T., On elliptic modular surfaces.J. Math. Soc. Japan, 24 (1972), 20–59.

    Article  MATH  MathSciNet  Google Scholar 

  • [ST]Salvati-Manni, R. &Top, J., Gusp forms of weight 2 for the group Γ2(4, 8).Amer. J. Math., 115, (1993), 455–486.

    MathSciNet  MATH  Google Scholar 

  • [Wi]Wirtinger, W.,Untersuchungen über Thetafunctionen. Teubner, Leipzig, 1895.

    Google Scholar 

  • [Zi]Ziegler, C., Jacobi forms of higher degree.Abh. Math. Sem. Univ. Hamburg, 59 (1989), 191–224.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Maz-Planck-Gesellschaft, Berlin, Germany

    Bernhard Runge

Authors
  1. Bernhard Runge
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Runge, B. Theta functions and Siegel-Jacobi forms. Acta Math. 175, 165–196 (1995). https://doi.org/10.1007/BF02393304

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02393304

Keywords

Search

Navigation