A new method for lower bounds of L-functions

Stephen Gelbart, Erez Lapid, Peter Sarnak

Type: Article

Publication Date: 2004-06-11

Citations: 27

DOI: https://doi.org/10.1016/j.crma.2004.04.024

Abstract

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). Soit L(s,π,r) une fonction L présente dans la théorie de Langlands–Shahidi. Nous prouvons une minoration de L(s,π,r) quand R(s)=1, en utilisant les séries d'Eisenstein. Cette méthode s'applique même lorsqu'on ne sait pas que L(s,π,r) est absolument convergente pour R(s)>1. Pour citer cet article : S.S. Gelbart et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).

Locations

Comptes Rendus Mathématique - View
French digital mathematics library (Numdam) - View - PDF
Comptes Rendus Mathématique - View
French digital mathematics library (Numdam) - View - PDF
Comptes Rendus Mathématique - View
French digital mathematics library (Numdam) - View - PDF

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