Proceedings of the Japan Academy, Series A, Mathematical Sciences
- Proc. Japan Acad. Ser. A Math. Sci.
- Volume 78, Number 6 (2002), 87-91.
A note on the mean value of the zeta and $L$-functions. XIII
Roelof Wichert Bruggeman and Yoichi Motohashi
Abstract
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.
Article information
Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 78, Number 6 (2002), 87-91.
Dates
First available in Project Euclid: 23 May 2006
Permanent link to this document
https://projecteuclid.org/euclid.pja/1148392681
Digital Object Identifier
doi:10.3792/pjaa.78.87
Mathematical Reviews number (MathSciNet)
MR1913937
Zentralblatt MATH identifier
1116.11066
Subjects
Primary: 11M06: $\zeta (s)$ and $L(s, \chi)$
Secondary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields
Keywords
Mean values of zeta-functions local functional equations of Jacquet-Langlands Gamma-functions of representations Bessel functions of representations
Citation
Bruggeman, Roelof Wichert; Motohashi, Yoichi. A note on the mean value of the zeta and $L$-functions. XIII. Proc. Japan Acad. Ser. A Math. Sci. 78 (2002), no. 6, 87--91. doi:10.3792/pjaa.78.87. https://projecteuclid.org/euclid.pja/1148392681