Mathematische Zeitschrift

, Volume 265, Issue 2, pp 263–276 | Cite as

Maass relations in higher genus

  • Shunsuke Yamana


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.


Ikeda lifting Saito–Kurokawa lifting Maass spaces Maass relations 

Mathematics Subject Classification (2000)



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  1. 1.
    Böcherer S.: Über die Fourierkoeffizienten der Siegelschen Eisensteinreihen. Manuscripta Math. 45, 273–288 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Eichler M.: Quadratische Formen und orthogonale Gruppen. Springer, Heiderberg (1952)zbMATHGoogle Scholar
  3. 3.
    Eichler M., Zagier D.: The Theory of Jacobi Forms. Progress in Mathematics, vol. 55. Birkhäuser, Boston (1985)Google Scholar
  4. 4.
    Feit P.: Explicit formulas for local factors in the Euler products for Eisenstein series. Nagoya Math. J. Vol. 113, 37–87 (1989)zbMATHMathSciNetGoogle Scholar
  5. 5.
    Ikeda T.: On the lifting of elliptic cusp forms to Siegel cusp forms of degree 2n. Ann. Math. 154, 641–681 (2001)zbMATHCrossRefGoogle Scholar
  6. 6.
    Katsurada H.: An explicit formula for Siegel series. Am. J. Math. 121, 415–452 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Kitaoka Y.: Dirichlet series in the theory of Siegel modular forms. Nagoya Math. J. 95, 73–84 (1984)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Kohnen W.: modular forms of half-integral weight to Siegel modular forms of even genus. Math. Ann. 322, 787–809 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Kohnen W., Kojima H.: A Maass space in higher genus. Compositio. Math. 141, 313–322 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Scharlau W.: Quadratic and Hermitian Forms. Springer, Berlin (1985)zbMATHGoogle Scholar
  11. 11.
    Ueda, M., Yamana, S.: On newforms for Kohnen plus spaces. Math. Z. (to appear)Google Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Graduate School of MathematicsKyoto UniversityKyotoJapan

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