We prove the recursive integral formula of class one -Whittaker functions on SL conjectured and verified in case of by Stade.
Nous montrons des formules intégrales récursives pour les fonctions de -Whittaker de classe un, qui ont été conjecturées (et vérifiées pour ) par Stade.
Keywords: Whittaker functions, automorphic forms
Mot clés : fonctions de Whittaker, formes automorphes
@article{AIF_2005__55_2_483_0, author = {Ishii, Taku}, title = {A remark on {Whittaker} functions on {SL}$(n,{\mathbb {R}})$}, journal = {Annales de l'Institut Fourier}, pages = {483--492}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {55}, number = {2}, year = {2005}, doi = {10.5802/aif.2104}, mrnumber = {2147897}, zbl = {1064.11040}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2104/} }
TY - JOUR AU - Ishii, Taku TI - A remark on Whittaker functions on SL$(n,{\mathbb {R}})$ JO - Annales de l'Institut Fourier PY - 2005 SP - 483 EP - 492 VL - 55 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2104/ DO - 10.5802/aif.2104 LA - en ID - AIF_2005__55_2_483_0 ER -
%0 Journal Article %A Ishii, Taku %T A remark on Whittaker functions on SL$(n,{\mathbb {R}})$ %J Annales de l'Institut Fourier %D 2005 %P 483-492 %V 55 %N 2 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2104/ %R 10.5802/aif.2104 %G en %F AIF_2005__55_2_483_0
Ishii, Taku. A remark on Whittaker functions on SL$(n,{\mathbb {R}})$. Annales de l'Institut Fourier, Volume 55 (2005) no. 2, pp. 483-492. doi : 10.5802/aif.2104. http://archive.numdam.org/articles/10.5802/aif.2104/
[1] Generalized Hypergeometric Series, Cambridge, 1935 | JFM | Zbl
[2] Automorphic Forms on , Lect. Notes in Math., Volume 1083 (1984) | MR | Zbl
[3] Whittaker functions on semisimple Lie groups, Hiroshima Math. J., Volume 12 (1982), pp. 259-293 | MR | Zbl
[4] Fonctions de Whittaker associées aux groupes de Chevalley, Bull. Soc. Math. France, Volume 95 (1967), pp. 243-309 | Numdam | MR | Zbl
[5] On Whittaker vectors and representation theory, Invent. Math., Volume 48 (1978), pp. 101-184 | DOI | MR | Zbl
[6] Automorphic Forms Constructed from Whittaker Vectors, J. of Funct. Anal., Volume 86 (1989), pp. 411-487 | DOI | MR | Zbl
[7] The multiplicity one theorem for , Ann. of Math., Volume 100 (1974), pp. 171-193 | DOI | MR | Zbl
[8] Poincaré Series For -Whittaker Functions, Duke Math. J., Volume 3 (1989), pp. 695-729 | MR | Zbl
[9] On Explicit Integral Formulas For -Whittaker Functions, Duke Math. J., Volume 60 (1990) no. 2, pp. 313-362 | DOI | MR | Zbl
[10] -Whittaker functions and hypergeometric series, Trans. Amer. Math. Soc., Volume 336 (1993) no. 1, pp. 253-264 | MR | Zbl
[11] The reciprocal of the beta function and Whittaker functions, Ann. Inst. Fourier, Grenoble, Volume 44 (1994) no. 1, pp. 93-108 | DOI | Numdam | MR | Zbl
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