Subconvexity for Rankin-Selberg \(L\)-functions of Maass forms.
The purpose of this paper is to give a subconvexity bound for Rankin-Selberg \(L\)-functions \(L(s,f\otimes g)\), where \(g\) is a fixed cusp form (holomorphic or real analytic) and \(f\) is a variable Maass cusp form with the spectral parameter tending to infinity. The forms are modular either for the full modular group or more generally for a congruence subgroup. An analogous subconvexity estimate was obtained by \textit{P. Sarnak} [J. Funct. Anal. 184 No. 2, 419--453 (2001; Zbl 1006.11022)] in the weight aspect if \(f\) is holomorphic. However, it was pointed out in the preprint ``Improvement to subconvexity bounds for Rankin-Selberg \(L\)-functions of cusp forms'' by \textit{Yuk-Kam Lau}, \textit{Jianya Liu} and \textit{Yangbo Ye} that there is a gap in the present paper so that the argument yields only a weaker estimate; nevertheless, it is stronger than the convexity bound. A better estimate is obtained in the above mentioned preprint.
scientific article; zbMATH DE number 1925570