A Fourier summation formula for the symmetric space $\mathrm{GL}\left(n\right)/\mathrm{GL}(n-1)$

 Access to full text

 Full (PDF)

1. [A] J. Arthur, A trace formula for reductive groups. [A1] I. Terms associated to classes in G(Q), Duke Math. J.45 (1978), 911-952; [A2] II. Applications of a truncation operator, Compos. Math.40 (1980), 87-121. Zbl0499.10033MR518111
2. [B] J. Bernstein, An operator Paley-Wiener theorem, in preparation. 
3. [BD] J. Bernstein, P. Deligne, Le centre de Bernstein, dans Représentation des groupes réductifs sur un corps local, Hermann, Paris (1984). Zbl0599.22016MR771671
4. [BZ] J. Bernstein, A. Zelevinskii, [BZ1] Representations of the group GL(n, F) where F is a nonarchimedean local field, Uspekhi Mat. Nauk31 (1976), 5-70; [BZ2] Induced representations of reductive p-adic groups. I, Ann. Sci. ENS10 (1977), 441-472. Zbl0412.22015MR425030
5. [Bi] F. Bien, D-modules and spherical representations, Princeton Univ. Press39 (1990). Zbl0723.22014MR1082342
6. [DP] G. van Dijk, M. Poel, The irreducible unitary GL(n — 1, R)-spherical representations of SL(n, R), Compos. Math.73 (1990), 1-30. Zbl0723.22018
7. [FJ] M. Flensted-Jensen, Discrete series for semi-simple symmetric spaces, Annals of Math.111 (1980), 253-311. Zbl0462.22006MR569073
8. [F] Y. Flicker, [F1] Twisted tensors and Euler products, Bull. Soc. Math. France116 (1988), 295-313; [F2] On distinguished representations, J. reine angew. Math. 418 (1991), 139-172; [F3] Distinguished representations and a Fourier summation formula, Bull. Soc. Math. France (1992); [F4] Cyclic automorphic forms on a unitary group, preprint. Zbl0725.11026MR984899
9. [FK] Y. Flicker, D. Kazhdan, A simple trace formula, J. Analyse Math.50 (1988), 189-200. Zbl0666.10018MR942828
10. [FKS] Y. Flicker, D. Kazhdan, G. Savin, Explicit realization of a metaplectic representation, J. Analyse Math.55 (1991), 17-39. Zbl0727.11021MR1094709
11. [GK] I. Gelfand, D. Kazhdan, Representations of GL(n, K) where K is a local field, in Lie groups and their representations, John Wiley and Sons (1975), 95-118. Zbl0348.22011
12. [G] P. Garrett, Decomposition of Eisenstein series. Rankin triple products, Ann. of Math.125 (1987), 209-235. Zbl0625.10020MR881269
13. [GP] B. Gross, D. Prasad, On the decomposition of a representation of SO(n) when restricted to SO(n — 1), preprint. Zbl0787.22018
14. [HK] M. Harris, S. Kudla, The central critical value of a triple product L-function, Ann. of Math.133 (1991), 605-672. Zbl0731.11031MR1109355
15. [J] H. Jacquet, [J1] Sur un résultat de Waldspurger, Ann. Sci. ENS.19 (1986), 185-229; [J2] On the nonvanishing of some L-functions, Proc. Indian Acad. Sci.97 (1987), 117-155. Zbl0659.10031MR868299
16. [JPS] H. Jacquet, I. Piatetski-Shapiro, J. Shalika, Rankin-Selberg convolutions, Amer. J. Math.105 (1983), 367-464. Zbl0525.22018MR701565
17. [JS] H. Jacquet, J. Shalika, [JS1] On Euler products and the classification of automorphic representations, Amer. J. Math.103 (1981), I: 499-558, II: 777-815; [JS2] Rankin-Selberg convolutions: Archimedean theory; in Festschrift in Honor of I. I. Piatetski-Shapiro, IMCP2 (1990), 125-207. Zbl0712.22011
18. [L] R. Langlands, On the functional equations satisfied by Eisenstein series, SLN544 (1976). Zbl0332.10018MR579181
19. [M] I. Macdonald, Symmetric functions and Hall polynomials, Oxford, Clarendon Press (1979). Zbl0487.20007MR553598
20. [MW] C. Moeglin, J.-L. Waldspurger, [MW1] Le spectre résiduel de GL(n), Ann. Sci. ENS22 (1989), 605-674; [MW2] Décomposition spectrale et series d'Eisenstein. Zbl0696.10023MR1026752
21. [Mo] L. Morris, Eisenstein series for reductive groups over global function fields, Canad. J. Math.34 (1982), I: 91-168, II: 1112-1182. Zbl0505.22017
22. [OM] T. Oshima, T. Matsuki, A description of discrete series for semisimple symmetric spaces, Advanced Studies in Pure Math. 4 (1984), 331-390. Zbl0577.22012MR810636
23. [PR] I. Piatetski - Shapiro, S.Rallis, Rankin triple L-functions, Compos. Math.64 (1987), 31-115. Zbl0637.10023MR911357
24. [P] D. Prasad, [P1] Trilinear forms for representations of GL(2) and local ε-factors, Compos. Math.75 (1990), 1-46; [P2] Invariant forms for representations of GL2 over a local field, Amer. J. Math. (1993); [P3] On the decomposition of a representation of GL(3) restricted to GL(2) over a p-adic field, Duke Math. J. (1993). 
25. [Sh] F. Shahidi, [Sh1] On certain L-functions, Amer. J. Math.103 (1981), 297-355; [Sh2] Local coefficients and normalization of intertwining operators for GL(n), Compos. Math.48 (1983), 271-295. Zbl0506.22020MR610479
26. [Sh] T. Shintani, On an explicit formula for class 1 "Whittaker functions" on GLn over p-adic fields, Proc. Japan Acad., 52 (1976), 180-182. Zbl0387.43002MR407208
27. [T] M. Tadic, Classification of unitary representations in irreducible representations of general linear group, Ann. Sci. ENS19 (1986), 335-382. Zbl0614.22005MR870688
28. [Th] E. Thoma, Die Einschränkung der Charaktere von GL(n, q) auf GL(n - 1, q), Math. Z.119(1971), 321-338. Zbl0202.02601MR288190
29. [W] J.-L. Waldspurger, [W1] Correspondence de Shimura, J. Math. Pure Appl.59 (1980), 1-113; [W2] Sur les coefficients de Fourier des formes modulaires de poids demi-entier, J. Math. Pure Appl.60 (1981), 375-484; [W3] Sur les valeurs de certaines fonctions L automorphes en leur centre de symetrie, Compos. Math.54 (1985), 173-242. Zbl0567.10021MR646366
30. [Z] A. Zelevinsky, Induced representations of reductive p-adic groups II. On irreducible representations of GL(n), Ann. Sci. ENS13 (1980), 165-210; [Z2] Representations of finite classical groups, SLN869 (1981). Zbl0441.22014MR584084
31. [Zh] D.P. Zhelobenko, Compact Lie groups and their representations, American Mathematical Society, Providence, 1973. Zbl0272.22006MR473098

1. Hervé Jacquet, Chen Nan, Positivity of quadratic base change $L$-functions