Positivity of 𝐋(1 2,π) for symplectic representations
[Positivité de L(1 2,π) pour représentations simplectiques]
Comptes Rendus. Mathématique, Tome 334 (2002) no. 2, pp. 101-104.

Soit π une représentation cuspidale géńerique de SO(2n+1). Nous prouvons que L(1 2,π)0.

Let π a cuspidal generic representation of SO(2n+1). We prove that L(1 2,π)0.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02217-3
Lapid, Erez 1 ; Rallis, Stephen 1

1 Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA
@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] Bushnell, C.J.; Henniart, G. 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] Deligne, P. 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] Fröhlich, A.; Queyrut, J. On the functional equation of the Artin L-function for characters of real representations, Invent. Math., Volume 20 (1973), pp. 125-138

[5] Ginzburg, D.; Rallis, S.; Soudry, D. On explicit lifts of cusp forms from GLm to classical groups, Ann. of Math. (2), Volume 150 (1999) no. 3, pp. 807-866

[6] Goldberg, D. Reducibility of induced representations for Sp(2n) and SO(n), Amer. J. Math., Volume 116 (1994) no. 5, pp. 1101-1151

[7] Guo, J. 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] Jacquet, H.; Nan, C. Positivity of quadratic base change L-functions, Bull. Soc. Math. France, Volume 129 (2001) no. 3, pp. 33-90

[9] Jacquet, H.; Shalika, J. 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] Jantzen, C. Reducibility of certain representations for symplectic and odd-orthogonal groups, Compositio Math., Volume 104 (1996) no. 1, pp. 55-63

[11] Katok, S.; Sarnak, P. Heegner points, cycles and Maass forms, Israel J. Math., Volume 84 (1993) no. 1–2, pp. 193-227

[12] Keys, C.D.; Shahidi, F. 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 L(1 2,π) for SO2n+1, Preprint

[14] Muić, G. A proof of Casselman–Shahidi's conjecture for quasi-split classical groups, Canad. Math. Bull., Volume 44 (2001) no. 3, pp. 298-312

[15] Prasad, D.; Ramakrishnan, D. 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] Shahidi, F. 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] Shahidi, F. Twisted endoscopy and reducibility of induced representations for p-adic groups, Duke Math. J., Volume 66 (1992) no. 1, pp. 1-41

[18] Tadić, M. On reducibility of parabolic induction, Israel J. Math., Volume 107 (1998), pp. 29-91

Cité par Sources :