Comptes Rendus
Number Theory
A new method for lower bounds of L-functions
Comptes Rendus. Mathématique, Volume 339 (2004) no. 2, pp. 91-94.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.04.024
Stephen S. Gelbart 1; Erez M. Lapid 2; Peter Sarnak 3, 4

1 Faculty of Mathematics and Computer Science, Nicki and J. Ira Harris Professorial Chair, The Weizmann Institute of Science, Rehovot 76100, Israel
2 Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
3 Department of Mathematics, Princeton University, Princeton, NJ, USA
4 The Courant Institute, New York, NY, USA
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Stephen S. Gelbart; Erez M. Lapid; Peter Sarnak. A new method for lower bounds of L-functions. Comptes Rendus. Mathématique, Volume 339 (2004) no. 2, pp. 91-94. doi : 10.1016/j.crma.2004.04.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.04.024/

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