Open Access
June 2002 A note on the mean value of the zeta and $L$-functions. XIII
Roelof Wichert Bruggeman, Yoichi Motohashi
Proc. Japan Acad. Ser. A Math. Sci. 78(6): 87-91 (June 2002). DOI: 10.3792/pjaa.78.87


Extending the discussion in the previous note [6] of this series, the group $\mathrm{PSL}_2(\mathbf{C})$ will be dealt with in place of $\mathrm{PSL}_2(\mathbf{R})$. We shall indicate that the functional structure that supports the spectral theory of Kloosterman sums in the complex case is essentially the same as in the real case, though it is more involved as can be expected.


Download Citation

Roelof Wichert Bruggeman. Yoichi Motohashi. "A note on the mean value of the zeta and $L$-functions. XIII." Proc. Japan Acad. Ser. A Math. Sci. 78 (6) 87 - 91, June 2002.


Published: June 2002
First available in Project Euclid: 23 May 2006

zbMATH: 1116.11066
MathSciNet: MR1913937
Digital Object Identifier: 10.3792/pjaa.78.87

Primary: 11M06
Secondary: 11F70

Keywords: Bessel functions of representations , Gamma-functions of representations , local functional equations of Jacquet-Langlands , Mean values of zeta-functions

Rights: Copyright © 2002 The Japan Academy

Vol.78 • No. 6 • June 2002
Back to Top