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Jan. 2002 A note on the mean value of the zeta and $L$-functions. XI
Matti Ilmari Jutila, Yoichi Motohashi
Proc. Japan Acad. Ser. A Math. Sci. 78(1): 1-6 (Jan. 2002). DOI: 10.3792/pjaa.78.1


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.


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Matti Ilmari Jutila. Yoichi Motohashi. "A note on the mean value of the zeta and $L$-functions. XI." Proc. Japan Acad. Ser. A Math. Sci. 78 (1) 1 - 6, Jan. 2002.


Published: Jan. 2002
First available in Project Euclid: 23 May 2006

zbMATH: 0998.11025
MathSciNet: MR1879854
Digital Object Identifier: 10.3792/pjaa.78.1

Primary: 11F66
Secondary: 11F72

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

Rights: Copyright © 2002 The Japan Academy

Vol.78 • No. 1 • Jan. 2002
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