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 187-234, [MR4654611](https://mathscinet.ams.org/mathscinet-getitem?mr=4654611), [Zbl 7752243](https://zbmath.org/7752243).

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