Proc. Japan Acad. Ser. A Math. Sci. 78 (1), 1-6, (Jan. 2002) DOI: 10.3792/pjaa.78.1
Matti Ilmari Jutila, Yoichi Motohashi
KEYWORDS: Hybrid subconvexity bound, Hecke $L$-function, Maass form, Bruggeman-Kuznetsov sum formula, binary additive divisor sum, 11F66, 11F72
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.