Proceedings of the Japan Academy, Series A, Mathematical Sciences

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

Matti Ilmari Jutila and Yoichi Motohashi

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The present note reports an optimal bound for a version of the spectral fourth power moment of Hecke $L$-functions associated with Maass forms over the full modular group, in which the spectral parameter runs over short intervals. Consequentially, a new hybrid subconvexity bound is attained for individual values of those $L$-functions on the critical line.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 78, Number 1 (2002), 1-6.

First available in Project Euclid: 23 May 2006

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Zentralblatt MATH identifier

Primary: 11F66: Langlands $L$-functions; one variable Dirichlet series and functional equations
Secondary: 11F72: Spectral theory; Selberg trace formula

Hybrid subconvexity bound Hecke $L$-function Maass form Bruggeman-Kuznetsov sum formula binary additive divisor sum


Jutila, Matti Ilmari; Motohashi, Yoichi. A note on the mean value of the zeta and $L$-functions. XI. Proc. Japan Acad. Ser. A Math. Sci. 78 (2002), no. 1, 1--6. doi:10.3792/pjaa.78.1.

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