## Tohoku Mathematical Journal

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

#### 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

https://projecteuclid.org/euclid.tmj/1113247179

Digital Object Identifier
doi:10.2748/tmj/1113247179

Mathematical Reviews number (MathSciNet)
MR1878927

Zentralblatt MATH identifier
1039.11027

#### 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

#### 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.

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