Skip to main content
Log in

Maass relations in higher genus

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

Abstract

For an arbitrary even genus 2n we show that the subspace of Siegel cusp forms of degree 2n generated by Ikeda lifts of elliptic cusp forms can be characterized by certain linear relations among Fourier coefficients. This generalizes the classical Maass relations in degree two to higher degrees.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Böcherer S.: Über die Fourierkoeffizienten der Siegelschen Eisensteinreihen. Manuscripta Math. 45, 273–288 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  2. Eichler M.: Quadratische Formen und orthogonale Gruppen. Springer, Heiderberg (1952)

    MATH  Google Scholar 

  3. Eichler M., Zagier D.: The Theory of Jacobi Forms. Progress in Mathematics, vol. 55. Birkhäuser, Boston (1985)

    Google Scholar 

  4. Feit P.: Explicit formulas for local factors in the Euler products for Eisenstein series. Nagoya Math. J. Vol. 113, 37–87 (1989)

    MATH  MathSciNet  Google Scholar 

  5. Ikeda T.: On the lifting of elliptic cusp forms to Siegel cusp forms of degree 2n. Ann. Math. 154, 641–681 (2001)

    Article  MATH  Google Scholar 

  6. Katsurada H.: An explicit formula for Siegel series. Am. J. Math. 121, 415–452 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  7. Kitaoka Y.: Dirichlet series in the theory of Siegel modular forms. Nagoya Math. J. 95, 73–84 (1984)

    MATH  MathSciNet  Google Scholar 

  8. Kohnen W.: modular forms of half-integral weight to Siegel modular forms of even genus. Math. Ann. 322, 787–809 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  9. Kohnen W., Kojima H.: A Maass space in higher genus. Compositio. Math. 141, 313–322 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  10. Scharlau W.: Quadratic and Hermitian Forms. Springer, Berlin (1985)

    MATH  Google Scholar 

  11. Ueda, M., Yamana, S.: On newforms for Kohnen plus spaces. Math. Z. (to appear)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shunsuke Yamana.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yamana, S. Maass relations in higher genus. Math. Z. 265, 263–276 (2010). https://doi.org/10.1007/s00209-009-0513-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00209-009-0513-z

Keywords

Mathematics Subject Classification (2000)

Navigation