Look at J. Bernstein, Erez Lapid - ["On the meromorphic continuation of Eisenstein series"](https://doi.org/10.1090/jams/1020), Journal of the American Mathematical Society (2023) Volume 37, Number 1, January 2024, Pages 187234.

(Also freely available as the preprint [arXiv:1911.02342v3](https://arxiv.org/abs/1911.02342v3).)