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.
"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. https://doi.org/10.3792/pjaa.78.1