V. Blomer and A. , Pohl: The sup-norm problem on the Siegel modular space of rank two, Amer. J. Math, p.23

A. Borel, Groupes Lineaires Algebriques, The Annals of Mathematics, vol.64, issue.1, pp.20-82, 1956.
DOI : 10.2307/1969949

H. Donnelly, Exceptional sequences of eigenfunctions for hyperbolic manifolds, Proc. AMS 135 no, pp.1551-1555, 2007.
DOI : 10.1090/S0002-9939-06-08613-8

A. Eskin and B. , Farb: Quasi-flats and rigidity in higher rank symmetric spaces, JAMS, vol.10, issue.3, pp.653-692, 1997.

B. Feigon, E. Lapid, and O. , On representations distinguished by unitary groups, Publications math??matiques de l'IH??S, vol.13, issue.1, pp.185-323, 2012.
DOI : 10.1007/s10240-012-0040-z

T. Finis and E. , Lapid: An approximation principle for congruence subgroups, p.22

R. Gangolli, On the Plancherel Formula and the Paley-Wiener Theorem for Spherical Functions on Semisimple Lie Groups, The Annals of Mathematics, vol.93, issue.1, pp.105-165, 1971.
DOI : 10.2307/1970758

B. Gross, On the motive of a reductive group, Inventiones Mathematicae, vol.130, issue.2, pp.287-313, 1997.
DOI : 10.1007/s002220050186

S. Helgason, Differential geometry, Lie groups, and symmetric spaces. Graduate studies in mathematics, pp.32-40, 2001.
DOI : 10.1090/gsm/034

S. Helgason, Geometric analysis on symmetric spaces, Mathematical Surveys and Monographs, vol.39, p.23, 2008.
DOI : 10.1090/surv/039

A. G. Helminck and S. P. Wang, On Rationality Properties of Involutions of Reductive Groups, Advances in Mathematics, vol.99, issue.1, pp.26-97, 1993.
DOI : 10.1006/aima.1993.1019

H. Iwaniec and P. , Sarnak: L ? norms of eigenfunctions of arithmetic surfaces, Ann. of Math, issue.2 2, pp.141-301, 1995.

H. Jacquet, Kloosterman identities over a quadratic extension II, Annales Scientifiques de l?????cole Normale Sup??rieure, vol.38, issue.4, pp.609-669, 2005.
DOI : 10.1016/j.ansens.2005.05.001

H. Jacquet, K. Lai, and S. , Rallis: A trace formula for symmetric spaces, Duke Math, J, vol.70, issue.2 5, pp.305-372, 1993.
DOI : 10.1215/s0012-7094-93-07006-8

R. Kottwitz, Stable trace formula: Elliptic singular terms, Mathematische Annalen, vol.39, issue.3, pp.365-400, 1986.
DOI : 10.1007/BF01458611

A. Knapp, Lie Groups Beyond an Introduction, Progress in Mathematics, vol.140, issue.34, p.36, 2002.
DOI : 10.1007/978-1-4757-2453-0

E. Lapid and O. Offen, Compact unitary periods, Compositio Mathematica, vol.143, issue.02, pp.323-338, 2007.
DOI : 10.1112/S0010437X06002612

. Marshall, Sup norms of Maass forms on semisimple groups, p.24

J. Matz and N. , Templier: Sato-Tate equidistribution for families of Hecke-Maass forms on SL, p.30

D. Milicevic, Large values of eigenfunctions on arithmetic hyperbolic 3-manifolds, GAFA 21 no, pp.1375-1418, 2011.

D. Nadler, Perverse sheaves on real loop Grassmannians, Inventiones mathematicae, vol.72, issue.1, pp.1-73, 2005.
DOI : 10.1007/s00222-004-0382-3

URL : http://arxiv.org/abs/math/0202150

Z. Rudnick and P. , The behaviour of eigenstates of arithmetic hyperbolic manifolds, Communications in Mathematical Physics, vol.55, issue.1, pp.195-213, 1994.
DOI : 10.1007/BF02099418

A. Saha, Large values of newforms on GL(2) with highly ramified central character Int, Math. Res. Not. (IMRN), issue.4, 2015.

Y. Sakellaridis, On the unramified spectrum of spherical varieties over p-adic fields, Compositio Math, pp.978-1016, 2008.

Y. Sakellaridis, Spherical functions on spherical varieties, American Journal of Mathematics, vol.135, issue.5, pp.1291-1381, 2013.
DOI : 10.1353/ajm.2013.0046

URL : http://arxiv.org/abs/0905.4244

Y. Sakellaridis and A. , Venkatesh: Periods and harmonic analysis on spherical varieties

P. Sarnak, Letter to Morawetz

S. Shin and N. , Sato???Tate theorem for families and low-lying zeros of automorphic $$L$$ L -functions, Inventiones mathematicae, vol.62, issue.3, pp.1-177, 2016.
DOI : 10.1007/s00222-015-0583-y

N. Templier, Large values of modular forms, Cambridge Journal of Mathematics, vol.2, issue.1, pp.91-116, 2014.
DOI : 10.4310/CJM.2014.v2.n1.a3

L. Galilée, 99 avenue Jean Baptiste Clément, 93430 Villetaneuse, France E-mail address: brumley@math.univ-paris13