Hybrid subconvexity for Maass form symmetric-square L-functions

Recently R. Khan and M. Young proved a mean Lindel\"{o}f estimate for the second moment of Maass form symmetric-square L-functions L(sym² uⱼ,1/2+it) on the short interval of length G |tⱼ|1+ε/t2/3, where tⱼ is a spectral parameter of the corresponding Maass form. Their estimate yields a subconvexity estimate for L(sym² uⱼ,1/2+it) as long as |tⱼ|6/7+δ t<(2-δ)|tⱼ|. We obtain a mean Lindel\"{o}f estimate for the same moment in shorter intervals, namely for G |tⱼ|1+ε/t. As a corollary, we prove a subconvexity estimate for L(sym² uⱼ,1/2+it) on the interval |tⱼ|2/3+δ t |tⱼ|6/7-δ.