Geodesic
Subconvexity bounds for triple $L$-functions and representation theory
Joseph Bernstein1 ; Andre Reznikov2
1 School of Mathematical Sciences<br/>Tel Aviv University<br/>Ramat Aviv, Tel Aviv 69978<br/>Israel
2 Department of Mathematics<br/>Bar-Ilan University<br/>Ramat Gan 52900<br/>Israel
Annals of mathematics, Tome 172 (2010) no. 3, pp. 1679-1718.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We describe a new method to estimate the trilinear period on automorphic representations of $\operatorname{PGL}_2(\mathbb{R})$. Such a period gives rise to a special value of the triple $L$-function. We prove a bound for the triple period which amounts to a subconvexity bound for the corresponding special value of the triple $L$-function. Our method is based on the study of the analytic structure of the corresponding unique trilinear functional on unitary representations of $\operatorname{PGL}_2(\mathbb{R})$.
DOI : 10.4007/annals.2010.172.1679

Joseph Bernstein 1 ; Andre Reznikov 2

1 School of Mathematical Sciences<br/>Tel Aviv University<br/>Ramat Aviv, Tel Aviv 69978<br/>Israel
2 Department of Mathematics<br/>Bar-Ilan University<br/>Ramat Gan 52900<br/>Israel 
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Joseph Bernstein; Andre Reznikov. Subconvexity bounds for triple $L$-functions and representation theory. Annals of mathematics, Tome 172 (2010) no. 3, pp. 1679-1718. doi : 10.4007/annals.2010.172.1679. http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.172.1679/

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