Burgess-like subconvex bounds for $GL_2 \times GL_1$

Abstract

We give a Burgess-like subconvex bound for $L(s, \pi \otimes \chi)$ in terms of the analytical conductor of $\chi$, where $\pi$ is a $GL_2$ cuspidal representation and $\chi$ is a Hecke character.Comment: to appear in Geometric and Functional Analysi