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Recurrence relations in the theory of Hecke operators

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Abstract

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.

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Literature cited

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

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

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

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

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Additional information

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

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Gritsenko, V.A. Recurrence relations in the theory of Hecke operators. J Math Sci 26, 2342–2348 (1984). https://doi.org/10.1007/BF01680014

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Keywords

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