Proceedings of the Japan Academy, Series A, Mathematical Sciences

A note on the mean value of the zeta and $L$-functions. XIII

Roelof Wichert Bruggeman and Yoichi Motohashi

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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.

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Proc. Japan Acad. Ser. A Math. Sci., Volume 78, Number 6 (2002), 87-91.

First available in Project Euclid: 23 May 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11M06: $\zeta (s)$ and $L(s, \chi)$
Secondary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields

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


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.

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