A new method for lower bounds of L-functions

Let $L(s\text{,}\pi \text{,}r)$ be an L-function which appears in the Langlands–Shahidi theory. We give a lower bound for $L(s\text{,}\pi \text{,}r)$ when $\mathfrak{R}(s)=1$ using Eisenstein series. This method is applicable even when $L(s\text{,}\pi \text{,}r)$ is not known to be absolutely convergent for $\mathfrak{R}(s)>1$. To cite this article: S.S. Gelbart et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).