Soit π une représentation cuspidale géńerique de SO(2n+1). Nous prouvons que .
Let π a cuspidal generic representation of SO(2n+1). We prove that .
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@article{CRMATH_2002__334_2_101_0, author = {Lapid, Erez and Rallis, Stephen}, title = {Positivity of $ \mathbf{L(}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{,\pi )}$ for symplectic representations}, journal = {Comptes Rendus. Math\'ematique}, pages = {101--104}, publisher = {Elsevier}, volume = {334}, number = {2}, year = {2002}, doi = {10.1016/S1631-073X(02)02217-3}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/S1631-073X(02)02217-3/} }
TY - JOUR AU - Lapid, Erez AU - Rallis, Stephen TI - Positivity of $ \mathbf{L(}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{,\pi )}$ for symplectic representations JO - Comptes Rendus. Mathématique PY - 2002 SP - 101 EP - 104 VL - 334 IS - 2 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(02)02217-3/ DO - 10.1016/S1631-073X(02)02217-3 LA - en ID - CRMATH_2002__334_2_101_0 ER -
%0 Journal Article %A Lapid, Erez %A Rallis, Stephen %T Positivity of $ \mathbf{L(}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{,\pi )}$ for symplectic representations %J Comptes Rendus. Mathématique %D 2002 %P 101-104 %V 334 %N 2 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S1631-073X(02)02217-3/ %R 10.1016/S1631-073X(02)02217-3 %G en %F CRMATH_2002__334_2_101_0
Lapid, Erez; Rallis, Stephen. Positivity of $ \mathbf{L(}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{,\pi )}$ for symplectic representations. Comptes Rendus. Mathématique, Tome 334 (2002) no. 2, pp. 101-104. doi : 10.1016/S1631-073X(02)02217-3. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02217-3/
[1] Calculs de facteurs epsilon de paires pour GLn sur un corps local. I, Bull. London Math. Soc., Volume 31 (1999) no. 5, pp. 534-542
[2] Cogdell J., Kim H., Piatetski-Shapiro I., Shahidi F., On lifting from classical groups to GLn, Preprint, 2000
[3] Les constantes locales de l'équation fonctionnelle de la fonction L d'Artin d'une représentation orthogonale, Invent. Math., Volume 35 (1976), pp. 299-316
[4] On the functional equation of the Artin L-function for characters of real representations, Invent. Math., Volume 20 (1973), pp. 125-138
[5] On explicit lifts of cusp forms from GLm to classical groups, Ann. of Math. (2), Volume 150 (1999) no. 3, pp. 807-866
[6] Reducibility of induced representations for Sp(2n) and SO(n), Amer. J. Math., Volume 116 (1994) no. 5, pp. 1101-1151
[7] On the positivity of the central critical values of automorphic L-functions for GL(2), Duke Math. J., Volume 83 (1996) no. 1, pp. 157-190
[8] Positivity of quadratic base change L-functions, Bull. Soc. Math. France, Volume 129 (2001) no. 3, pp. 33-90
[9] Exterior square L-functions, Automorphic Forms, Shimura Varieties, and L-Functions, Vol. II (Ann Arbor, MI, 1988), Academic Press, Boston, MA, 1990, pp. 143-226
[10] Reducibility of certain representations for symplectic and odd-orthogonal groups, Compositio Math., Volume 104 (1996) no. 1, pp. 55-63
[11] Heegner points, cycles and Maass forms, Israel J. Math., Volume 84 (1993) no. 1–2, pp. 193-227
[12] Artin L-functions and normalization of intertwining operators, Ann. Sci. École Norm. Sup. (4), Volume 21 (1988) no. 1, pp. 67-89
[13] Lapid E., Rallis S., On the non-negativity of for SO2n+1, Preprint
[14] A proof of Casselman–Shahidi's conjecture for quasi-split classical groups, Canad. Math. Bull., Volume 44 (2001) no. 3, pp. 298-312
[15] On the global root numbers of GL(n)×GL(m), Automorphic Forms, Automorphic Representations, and Arithmetic (Fort Worth, TX, 1996), American Mathematical Society, Providence, RI, 1999, pp. 311-330
[16] A proof of Langlands' conjecture on Plancherel measures; complementary series for p-adic groups, Ann. of Math. (2), Volume 132 (1990) no. 2, pp. 273-330
[17] Twisted endoscopy and reducibility of induced representations for p-adic groups, Duke Math. J., Volume 66 (1992) no. 1, pp. 1-41
[18] On reducibility of parabolic induction, Israel J. Math., Volume 107 (1998), pp. 29-91
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