On the growth of Rankin-Selberg L-functions for $SL(2)$

Abstract

In this paper, we establish bounds of the Rankin-Selberg $L$-function for $SL(2)$ using the supnorm of the Eisenstein series and a purely representation theoretic index over the real group. Consequently, we obtain a subconvexity bound $L(\frac{1}{2}+it,f_1\times f_2)\le C(1+|t|{)}^{\frac{5}{6}+\epsilon }$ for two Maass cusp forms of $SL(2,\mathbb{Z})$.

References in corpus (2)

• A note on the sup norm of Eisenstein series
• Hybrid subconvexity for class group $L$-functions and uniform sup norm bounds of Eisenstein series