[Valeurs spéciales de fonctions L pour les groupes orthogonaux]
Dans cette Note, nous présentons des résultats de rationalité pour les valeurs critiques des fonctions L de degré 2n, attachées à sur , où n est un entier positif. La preuve résulte d'une étude de la cohomologie d'Eisenstein de rang un, pour .
This is an announcement of certain rationality results for the critical values of the degree-2n L-functions attached to over for an even positive integer n. The proof follows from studying the rank-one Eisenstein cohomology for .
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@article{CRMATH_2017__355_3_263_0,
author = {Chandrasheel Bhagwat and A. Raghuram},
title = {Special values of {\protect\emph{L}-functions} for orthogonal groups},
journal = {Comptes Rendus. Math\'ematique},
pages = {263--267},
publisher = {Elsevier},
volume = {355},
number = {3},
year = {2017},
doi = {10.1016/j.crma.2017.01.016},
language = {en},
}
Chandrasheel Bhagwat; A. Raghuram. Special values of L-functions for orthogonal groups. Comptes Rendus. Mathématique, Volume 355 (2017) no. 3, pp. 263-267. doi : 10.1016/j.crma.2017.01.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.01.016/
[1] The Endoscopic Classification of Representations: Orthogonal and Symplectic Groups, American Mathematical Society Colloquium Publications, vol. 61, American Mathematical Society, Providence, RI, USA, 2013
[2] Generic transfer for general spin groups, Duke Math. J., Volume 132 (2006) no. 1, pp. 137-190
[3] Appendix to Orloff Critical values of certain tensor product L-functions, Invent. Math., Volume 90 (1987) no. 1, pp. 181-188
[4] Valeurs de fonctions L et périodes d'intégrales, Proc. Sympos. Pure Math., XXXIII, Automorphic Forms, Representations and L-functions, Amer. Math. Soc., Providence, RI (1979), pp. 313-346 (French). With an appendix by N. Koblitz and A. Ogus, Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, OR, USA, 1977 Part 2
[5] Arithmeticity for periods of automorphic forms, Automorphic Representations and L-functions, Tata Inst. Fundam. Res. Stud. Math., vol. 22, Tata Inst. Fund. Res., Mumbai, 2013, pp. 187-229
[6] Harish-Chandra modules over , 2014 (Preprint, available at) | arXiv
[7] Eisenstein cohomology and ratios of critical values of Rankin–Selberg L-functions, C. R. Acad. Sci. Paris Ser. I, Volume 349 (2011) no. 13–14, pp. 719-724
[8] Eisenstein cohomology for and ratios of critical values of Rankin–Selberg L-functions, 2015 (Including Appendix 1 by Uwe Weselmann, and Appendix 2 by Chandrasheel Bhagwat and A. Raghuram. Preprint available at) | arXiv
[9] Descent construction for GSpin groups, Mem. Amer. Math. Soc., Volume 243 (2016) no. 1148
[10] On local L-functions and normalized intertwining operators, Can. J. Math., Volume 57 (2005) no. 3, pp. 535-597
[11] Le spectre résiduel de GL(n). (French), Ann. Sci. Éc. Norm. Supér. (4), Volume 22 (1989) no. 4, pp. 605-674
[12] Local coefficients as Artin factors for real groups, Duke Math. J., Volume 52 (1985) no. 4, pp. 973-1007
[13] On the periods of modular forms, Math. Ann., Volume 229 (1977) no. 3, pp. 211-221
[14] The special values of the zeta functions associated with Hilbert modular forms, Duke Math. J., Volume 45 (1978) no. 3, pp. 637-679
[15] Reducibility of generalized principal series representations, Acta Math., Volume 145 (1980) no. 3–4, pp. 227-299
[16] La formule de Plancherel pour les groupes p-adiques (d'après Harish-Chandra), J. Inst. Math. Jussieu, Volume 2 (2003) no. 2, pp. 235-333
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