Tohoku Mathematical Journal

A certain class of Poincaré series on {${\rm Sp}\sb n$}. {II}

Winfried Kohnen and Jyoti Sengupta

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Abstract

We compute the Petersson scalar product of certain Poincaré series introduced in our previous paper against a Siegel cusp form and show that it can be written as a certain averaged cycle integral. This generalizes earlier work by Katok, Zagier and the first named author in the case of genus 1.

Article information

Source
Tohoku Math. J. (2), Volume 54, Number 1 (2002), 61-69.

Dates
First available in Project Euclid: 11 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1113247179

Digital Object Identifier
doi:10.2748/tmj/1113247179

Mathematical Reviews number (MathSciNet)
MR1878927

Zentralblatt MATH identifier
1039.11027

Subjects
Primary: 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms

Citation

Kohnen, Winfried; Sengupta, Jyoti. A certain class of Poincaré series on {${\rm Sp}\sb n$}. {II}. Tohoku Math. J. (2) 54 (2002), no. 1, 61--69. doi:10.2748/tmj/1113247179. https://projecteuclid.org/euclid.tmj/1113247179


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References

  • S. Katok, Closed geodesics, periods and arithmetic of modular forms, Invent. Math. 80 (1985), 469--480.
  • W. Kohnen and D. Zagier, Modular forms with rational periods, Modular Forms (ed. R. A. Rankin), 197--249, Ellis Horwood, Chichester, 1984.
  • W. Kohnen, Special quadratic forms, Siegel modular groups and Siegel modular varieties, Internat. J. Math. 1 (1990), 397--429.
  • W. Kohnen and J. Sengupta, A certain class of Poincaré series on $Sp_n$, Internat. J. Math. 10 (1999), 425--433.
  • C.-L. Siegel, Symplectic Geometry, Collected Works II (eds. K. Chandrasekharan, H. Maaß), 274--359, Springer, Berlin-Heidelberg-New York, 1966.
  • A. Terras, Harmonic Analysis on Symmetric spaces and Applications II, Springer, Berlin-Heidelberg-New York, 1988.
  • D. Zagier, Modular forms whose Fourier coefficients involve zeta-functions of quadratic fields, Modular functions of one variable VI (eds. J.-P. Serre, D. Zagier), 106--169, Lecture Notes in Math. 627, Springer, Berlin-Heidelberg-New York, 1977.

See also

  • Related Article: A certain class of Poincaré series on ${\rm Sp}\sb n$. Internat. J. Math. 10 (1999), no. 4, 425--433.