Positivity of quadratic base change L-functions

Bulletin de la Societe Mathematique de France

Volumn 129, Issue 1, 2001, Pages 33-90

  Jacquet, Hervé ^a   Nan, Chen ^a  

^a MC 4408 ^*  (United States)

Author keywords

L functions; Positivity; Quadratic base change

Indexed keywords

EID: 0037908399     PISSN: 00379484     EISSN: None     Source Type: Journal    
DOI: 10.24033/bsmf.2386     Document Type: Article

References (39)

1. ASAI (T.) - On certain Dirichlet series associated with Hilbert modular forms, Math. Ann., t. 226 (1977), pp. 81-94.
2. ARTHUR (J.) - A trace formula for reductive groups I: Terms associated to classes in G(ℚ), Duke Math. J., t.45 (1978), 911-952.
3. BERNSTEIN (J.) - P-invariant distributions of Gl(n) and the classification of unitary representations of Gl(n) (non Archimedean case), in Lie Group Representations II, College Park, Md., 1982/1983, Lecture Notes in Math. 1041. Springer-Verlag, 1984.
4. BUMP (D.), FRIEDBERG (S.), HOFFSTEIN (J.) - Eisenstein series on the metaplectic group and non-vanishing theorems for automorphic L-functions, Ann. of Math., t. 131 (1990), pp. 53-127.
5. BARUCH (E.M.), MAO (Z.) - Central critical value of automorphic L-functions, preprint
6. CASSELMAN (W.), HECHT (H.), MILIČIC (D.) - Bruhat filtrations and Whittaker vectors for real groups, preprint.
7. DIXMIER (J.), MALLIAVIN (P.) - Factorizations de fonctions et vecteurs indéfiniment différentiables. Bull. Soc. Math. France, t. 102 (1978), pp. 305-330.
8. FLICKER (Y.) - Twisted tensors and Euler products, Bull. Soc. Math. France, t. 116 (1988), pp. 295-313.
9. FLICKER (Y.) - On distinguished representations, J. reine angew Math., t. 418 (1991), pp. 139-172.
10. FLICKER (Y.) - A Fourier summation formula for the symmetric space Gl(n)/Gl(n - 1), Comp. Math., t. 88 (1992), pp. 39-117.
11. FLICKER (Y.) - Orbital Integrals on symmetric spaces and spherical characters, J. Algebra, t. 184 (1996), pp. 705-754.
12. FLICKER (Y.), ZINONIEV (D.) - On the poles of twisted L-functions, Proc. Japan Acad. Sci., t. 71 (1995), pp. 114-116.
13. FRIEDBERG (S.), HOFFSTEIN (J.) - Non vanishing theorem for automorphic L-functions for Gl(2), Ann. of Math., t. 142 (1995), pp. 385-423.
14. GUO (J.) - On the positivity of the central critical value of automorphic L-functions for Gl(2), Duke Math. J., t. 83 (1996), pp. 157-189.
15. GUO (J.) - On a generalization of a result of Waldspurger, Canad. J. Math., t. 48 (1996), pp. 105-142.
16. GROSS (B.) - Heights and the special values of L series, in Number Theory (Montreal, Que., 1985), 115-187, CMS Conf. Proc. 7, Americ. Math. Soc., Providence, RI, 1987.
17. GROSS (B.), ZAGIER (D.) - Heegner points and derivatives of automorphic L-functions for Gl(2), Invent. Math., t. 84 (1986), pp. 225-320.
18. HAKIM (J.) - Distinguished p-adic representations, Duke Math. J., t. 62 (1991), pp. 1-22.
19. HARDER (G.), LANGLANDS (R.P.), RAPOPORT (M.) - Algebraische Zyklen auf Hilbert - Blumenthal-Flächen, J. reine angew. Math., t. 366 (1986), pp. 53-120.
20. JACQUET (H.) - Sur un résultat de Waldspurger, Ann. Scient. École Norm. Sup., t. 19 (1986), pp. 185-229.
21. JACQUET (H.) - Sur un résultat de Waldspurger II, Comp. Math., t. 63 (1987), pp. 315-389.
22. JACQUET (H.), LAI (K.) - A relative trace formula, Comp. Math., t. 54 (1995), pp. 243-310.
23. JACQUET (H.), LAI (K.), RALLIS (S.) A trace formula for symmetric spaces, Duke Math. J., t. 70 (1993), pp. 305-371.
24. JACQUET (H.), LAPID (E.), ROGAWSKI (J.) - Periods of automorphic forms, J. Amer. Math. Soc., t. 12 (1999). pp. 173-240.
25. JACQUET (H.), YE (Y.) - Une remarque sur le changement de base quadratique, C. R. Acad. Sci. Paris Sér. I Math., t. 311 (1990), pp. 671-676.
26. KHONEN (W.) - Fourier coefficients of modular forms of half integral weight, Math. Ann., t. 271 (1985), pp. 237-268.
27. KAMAL KHURI-MAKDSI - On the Fourier coefficients of non holomorphic Hilbert modular forms of half integral weight, Duke Math. J., t. 84 (1996), pp. 399-452.
28. KATOK (S.), SARNAK (P.) - Heegner points, cycles, and Maass forms, Israel J. Math., t. 84 (1993), pp. 193-227.
29. KOHNEN (W.), ZAGIER (D.) - Values of L-series of modular forms at the center of the critical strip, Invent. Math., t. 64 (1981), pp. 175-198.
30. ROHRLICH (D.) - Non vanishing of L-functions for Gl(2), Invent. Math., t. 97 (1989), pp. 381-403.
31. RADER (C.), RALLIS (S.) - Spherical characters on p-adic symmetric spaces, Amer. J. Math., t. 118 (1996), pp. 91-178.
32. SHIMURA (S.) - On Fourier coefficients of Hilbert modular forms of half-integral weight, Duke Math. J., t. 71 (1993), pp. 501-557.
33. WALDSPURGER (J.-L.) - Corespondances de Shimura, J. Math. Pures Appl., t. 59 (1980), pp. 1-132.
34. WALDSPURGER (J.-L.) - Sur les coefficients de Fourier des formes modulaires de poids demi-entier, J. Math. Pures Appl., t. 60 (1981), pp. 375-484.
35. WALDSPURGER (J.-L.) - Quelques propriétés arithmétiques de certaines formes automorphes sur Gl(2), Comp. Math., t. 54 (1985), pp. 121-171.
36. WALDSPURGER (J.-L.) - Sur les valeurs de fonctions L-automorphes en leur centre de symétrie, Comp. Math., t. 54 (1985), pp. 173 -242.
37. WALDSPURGER (J.-L.) - Correspondances de Shimura et quaternions, Forum Math., t. 3 (1991), pp. 219-307.
38. WALLACH (N.) - Real Reductive Groups II, Pure and Applied Mathematics, Vol 132-II (1192), Academic Press.
39. YANG (T.) - Theta liftings and Hecke L-functions, J. reine angew. Math., t.485 (1997), pp. 25-53.