Abstract
Our purpose is to obtain a geometric formula as explicit as possible for the L 2 index of a Dirac operator over a locally symmetric space of finite volume, generalizing Arthur’s formula for the Euler–Poincaré caracteristic (Arthur in Invent Math 97:257–290, 1989).
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Bibliographie
Arthur J. (1988). The invariant trace formula. II. Global theory. JAMS 1: 501–554
Arthur J. (1989). Intertwinng operators and residues II. Invariant distributions. Compos. Math. 70: 51–99
Arthur J. (1989). The L 2-Lefschetz Numbers of Hecke Operators. Invent. Math. 97: 257–290
Arthur J. (1993). On elliptic tempered characters. Acta Math. 171: 73–138
Arthur J. (1994). On the Fourier transform of weighted orbital integrals. J. Reine Angew. Math. 452: 163–217
Arthur J. (2002). A stable trace formula. I. J. Inst. Math. Jussieu 1: 175–277
Arthur J. (2001). A stable trace formula. II. Invent. Math. 143: 157–220
Arthur J. (2003). A stable trace formula. III. Ann. Math. 158(2): 769–873
Atiyah M.F., Donnelly H., Singer I.M. (1983). Eta invariants, signature defects of cusps, and values of L-functions. Ann. Math. 118: 131–177
Barbasch D., Moscovici H. (1983). L 2-index and the Selberg trace formula. J. Funct. Anal. 53: 151–201
Clozel L., Delorme P. (1985). Pseudo coefficients et cohomologie des groupes réductifs. C. R. Acad. Sci. Paris 300: 385–387
Duflo M., Labesse J.-P. (1971). Sur la formule des traces de Selberg. Ann. Sci. ENS 4: 193–284
Goresky M., Kottwitz R., MacPherson R. (1997). Discrete series characters and the Lefschetz formula for Hecke operators. Duke Math. J. 89(3): 477–554
Harish-Chandra.: Supertempered distributions on real reductive groups. Collected Papers, vol. IV, pp. 447–461 (1983)
Labesse J.-P. (1991). Pseudo-coefficients très cuspidaux et K-théorie. Math. Ann. 291: 607–616
Labesse, J.-P.: Snowbird Lectures. Préprint (2006)
Langlands R.P., Shelstad D. (1987). On the definition of transfer factors. Math. Ann. 279: 219–271
Langlands, R.P., Shelstad, D.: Descent for transfer factors, pp. 485–563. The Grothendieck Festschrift II, Birkhäuser (1991)
Miatello R. (1982). Alternating sum formula for multiplicities in \(L^2(\Gamma\backslash G)\). Trans. Am. Math. Soc. 269: 129–138
Moscovici H. (1982). L 2-index of elliptic operators on locally symmetric spaces of finite volume. Contemp. Math. A.M.S. 10: 129–138
Müller W. (1984). Signature defects of cusps of Hilbert modular varieties and values of L-series at s = 1. J. Differ. Geom. 20(1): 55–119
Ngô, B.C.: Le lemme fondamental pour les algèbres de Lie. Préprint (2007)
Shelstad D. (1979). Characters and inner forms of a quasi-split group over \({\mathbb{R}}\). Compos. Math. 39: 11–45
Shelstad D. (1979). Orbital integrals and a family of groups attached to a real reductive group. Ann. Sci. ENS 12: 1–31
Shelstad D. (1982). L-Indistinguishability for real groups. Math. Ann. 259: 385–430
Waldspurger J.-L. (1997). Le lemme fondamental implique le transfert. Compos. Math. 105: linebreak 153–236
Waldspurger J.-L. (2006). Endoscopie et changement de caractéristique. J. Inst. Math. Jussieu 5: 423–525
Waldspurger, J.-L.: L’endoscopie tordue n’est pas si tordue, Analyse harmonique. Prépublication (2006)