Proceedings of the Japan Academy, Series A, Mathematical Sciences

A spectral decomposition of the product of four zeta-values

Yoichi Motohashi

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Proc. Japan Acad. Ser. A Math. Sci., Volume 65, Number 5 (1989), 143-146.

First available in Project Euclid: 19 November 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11M06: $\zeta (s)$ and $L(s, \chi)$
Secondary: 11F37: Forms of half-integer weight; nonholomorphic modular forms


Motohashi, Yoichi. A spectral decomposition of the product of four zeta-values. Proc. Japan Acad. Ser. A Math. Sci. 65 (1989), no. 5, 143--146. doi:10.3792/pjaa.65.143.

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  • [1] F. V. Atkinson: The mean-value of the Riemann zeta-function. Acta Math., 81, 353-376 (1949).
  • [2] N. V. Kuznecov: Petersson's conjecture for cusp forms of weight zero and Linnik's conjecture. Sums of Kloosterman sums. Math., USSR Sbornik, 39, 299-342 (1981).
  • [3] N. V. Kuznecov: Convolution of the Fourier coefficients of the Eisenstein-Maass series. Zap. Nauch. Sem., LOMI, 129, 43-84 (1983) (in Russian).
  • [4] Y. Motohashi: A note on the mean value of the zeta and L-functions. V. Proc, Japan Acad., 62A, 399-401 (1986).
  • [5] N. I. Zavorotni: On the fourth power moment of the zeta-function. (preprint) (in Russian).