Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Recurrence relations in the theory of Hecke operators

  • 28 Accesses

  • 1 Citations


In this paper one computes the“−2 power” of the Frobenius element of the Hecke ring of the subgroup ⌈n,1(q) of a modular group of genus n+1, which is the semidirect product of the Heisenberg group and the modular group ⌈n(q) of genusn.

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

Literature cited

  1. 1.

    A. N. Andrianov,“The multiplicative arithmetic of Siegel modular forms,” Usp. Mat. Nauk,34, No. 1, 67–135 (1979).

  2. 2.

    V. A. Gritsenko,“The action of modular operators on the Fourier-Jacobi coefficients of modular forms,” Mat. Sb.,119, No. 2, 248–278 (1982).

  3. 3.

    G. Shimura,“Arithmetic of alternating forms and quaternion Hermitian forms,” J. Math. Soc. Jpn.,15, No. 1, 33–65 (1963).

  4. 4.

    I. Satake,“Theory of spherical functions on reductive algebraic groups over p-adic fields,” Publ. Math. IHES, No. 18, 5–70 (1963).

Download references

Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 125, pp. 65–73, 1983.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Gritsenko, V.A. Recurrence relations in the theory of Hecke operators. J Math Sci 26, 2342–2348 (1984).

Download citation


  • Recurrence Relation
  • Heisenberg Group
  • Semidirect Product
  • Modular Group
  • Frobenius Element