Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T03:13:52.715Z Has data issue: false hasContentIssue false
  • English
  • Français

On the continuity of Arthur’s trace formula: the semisimple terms

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  06 April 2011

Tobias Finis  and
Erez Lapid
Tobias Finis
Affiliation:
Mathematisches Institut der Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225, Düsseldorf, Germany (email: finis@math.uni-duesseldorf.de)
Erez Lapid
Affiliation:
Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel (email: erezla@math.huji.ac.il)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that the semisimple part of the trace formula converges for a wide class of test functions.

Keywords

trace formula

MSC classification

Secondary: 11F72: Spectral theory; Selberg trace formula
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 3 , May 2011 , pp. 784 - 802
Copyright
Copyright © Foundation Compositio Mathematica 2011

References

[1]Arthur, J., A trace formula for reductive groups. I. Terms associated to classes in G(Q), Duke Math. J. 45 (1978), 911–952; MR 18111(80d:10043).CrossRefGoogle Scholar
[2]Arthur, J., A measure on the unipotent variety, Canad. J. Math. 37 (1985), 1237–1274; MR 828844(87m:22049).CrossRefGoogle Scholar
[3]Arthur, J., On a family of distributions obtained from orbits, Canad. J. Math. 38 (1986), 179–214; MR 835041(87k:11058).CrossRefGoogle Scholar
[4]Arthur, J., An introduction to the trace formula, in Harmonic analysis, the trace formula, and Shimura varieties, Clay Mathematics Proceedings, vol. 4 (American Mathematical Society, Providence, RI, 2005), 1–263; MR 2192011.Google Scholar
[5]Finis, T. and Lapid, E., On the Arthur–Selberg trace formula for GL(2), Groups Geom. Dyn. 5(2) (2011) (special issue on the occasion of Fritz Grunewald’s 60th birthday), 367–391.CrossRefGoogle Scholar
[6]Finis, T., Lapid, E. and Müller, W., The spectral side of Arthur’s trace formula, Proc. Natl. Acad. Sci. USA 106 (2009), 15563–15566.CrossRefGoogle ScholarPubMed
[7]Harish-Chandra, , Automorphic forms on semisimple Lie groups, Lecture Notes in Mathematics, vol. 62 (Springer, Berlin, 1968); MR 0232893(38#1216), Notes by J. G. M. Mars.CrossRefGoogle Scholar
[8]Hoffmann, W., Geometric estimates for the trace formula, Ann. Global Anal. Geom. 34 (2008), 233–261; MR 2434856(2009e:11100).CrossRefGoogle Scholar
[9]Humphreys, J. E., Linear algebraic groups, Graduate Texts in Mathematics, vol. 21 (Springer, New York, 1975); MR 0396773(53#633).CrossRefGoogle Scholar
[10]Langlands, R. P., The volume of the fundamental domain for some arithmetical subgroups of Chevalley groups, in Algebraic groups and discontinuous subgroups (Proceedings of Symposia in Pure Mathematics, Boulder, CO, 1965) (American Mathematical Society, Providence, RI, 1966), 143–148; MR 0213362(35#4226).CrossRefGoogle Scholar
[11]Mœglin, C. and Waldspurger, J.-L., Spectral decomposition and Eisenstein series, Cambridge Tracts in Mathematics, vol. 113 (Cambridge University Press, Cambridge, 1995);MR 1361168(97d:11083).CrossRefGoogle Scholar
[12]Mostow, G. D., Fully reducible subgroups of algebraic groups, Amer. J. Math. 78 (1956), 200–221; MR 0092928(19,1181f).CrossRefGoogle Scholar
[13]Selberg, A., Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. (N.S.) 20 (1956), 47–87; MR 0088511(19,531g).Google Scholar