A new method for lower bounds of L-functions

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