Theta dichotomy for unitary groups

Journal of the American Mathematical Society

Volumn 9, Issue 4, 1996, Pages 941-1004

  Harris, Michael ^a   Kudla, Stephen S ^b   Sweet, William J ^c  

^a BRANDEIS UNIVERSITY   (United States)

^b University of Maryland   (United States)

^c FLORIDA INTERNATIONAL UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030492982     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0894-0347-96-00198-1     Document Type: Article

References (97)

1. J. Adams, L-functoriality for dual pairs. Astérisque 171-172 (1989), 85-129. MR 91e:55016
2. J. Adams, L-functoriality for dual pairs. Astérisque 171-172 (1989), 85-129. MR 91e:55016
3. J. Arthur, On some problems suggested by the trace formula, Proc. of the Special Year in Harmonic Analysis, University of Maryland, Lecture Notes in Math. 1024, Springer-Verlag, New York, 1984. MR 85k:11025
4. J. Arthur, On some problems suggested by the trace formula, Proc. of the Special Year in Harmonic Analysis, University of Maryland, Lecture Notes in Math. 1024, Springer-Verlag, New York, 1984. MR 85k:11025
5. J. Arthur, Unipotent automorphic representations: conjectures. Orbites unipotentes et representations, II, Astérisque 171-172, 1989, pp. 13-73. MR 91f:22030
6. J. Arthur, Unipotent automorphic representations: conjectures. Orbites unipotentes et representations, II, Astérisque 171-172, 1989, pp. 13-73. MR 91f:22030
7. S. Brocco, On the non-vanishing of theta-liftings from U(1) to U(1), Ph.D. Thesis. Brandeis University (1992).
8. L. Clozel, Représentations Galoisiennes associées aux représentations automorphes autoduales de GL(n), Publ. Math. IHES 73 (1991), 97-145. MR 92i:11055
9. L. Clozel, Représentations Galoisiennes associées aux représentations automorphes autoduales de GL(n), Publ. Math. IHES 73 (1991), 97-145. MR 92i:11055
10. S. Gelbart and J. Rogawski, L-functions and Fourier-Jacobi coefficients for the unitary group U(3), Invent. Math. 105 (1991), 445-472. MR 93b:11059
11. S. Gelbart and J. Rogawski, L-functions and Fourier-Jacobi coefficients for the unitary group U(3), Invent. Math. 105 (1991), 445-472. MR 93b:11059
12. S. Gelbart and J. Rogawski, Exceptional representations and Shimura's integral for the local unitary group U(3), Festschrift in Honor of Piatetski-Shapiro, vol. 2, Israel Math. Conf. Proc., 1990, pp. 19-75. MR 93h:22029
13. S. Gelbart and J. Rogawski, Exceptional representations and Shimura's integral for the local unitary group U(3), Festschrift in Honor of Piatetski-Shapiro, vol. 2, Israel Math. Conf. Proc., 1990, pp. 19-75. MR 93h:22029
14. S. Gelbart, J. Rogawski and D. Soudry, On the genericity of endoscopic L-packets on U(3), preprint.
15. S. Gelbart, J. Rogawski and D. Soudry, On periods of cusp forms and algebraic cycles for U(3), Israel J. Math. 83 (1993), 213-252. MR 95a:11047
16. S. Gelbart, J. Rogawski and D. Soudry, On periods of cusp forms and algebraic cycles for U(3), Israel J. Math. 83 (1993), 213-252. MR 95a:11047
17. S. Gelbart, J. Rogawski and D. Soudry, Periods of cusp forms and L-packets, C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), 717-722. MR 94m:11064
18. S. Gelbart, J. Rogawski and D. Soudry, Periods of cusp forms and L-packets, C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), 717-722. MR 94m:11064
19. R. Godement and H. Jacquet, Zeta functions of simple algebras, Lecture Notes in Math. 260, Springer, New York, 1972. MR 49:7241
20. R. Godement and H. Jacquet, Zeta functions of simple algebras, Lecture Notes in Math. 260, Springer, New York, 1972. MR 49:7241
21. B. H. Gross, L-functions at the central critical point, Motives, part I, Proc. Symp. Pure Math., vol. 55, AMS, 1994, pp. 527-535. MR 95a:11060
22. B. H. Gross, L-functions at the central critical point, Motives, part I, Proc. Symp. Pure Math., vol. 55, AMS, 1994, pp. 527-535. MR 95a:11060
23. B. H. Gross and S. S. Kudla, Heights and the central critical values of triple product L-functions, Compositio Math. 81 (1992), 143-209. MR 93g:11047
24. B. H. Gross and S. S. Kudla, Heights and the central critical values of triple product L-functions, Compositio Math. 81 (1992), 143-209. MR 93g:11047
25. n-1, Canadian J. Math. 44 (1992), 974-1002. MR 93j:22031
26. n-1, Canadian J. Math. 44 (1992), 974-1002. MR 93j:22031
27. M. Harris, L-functions of 2 × 2 unitary groups and factorization of periods of Hilbert modular forms, Jour. AMS 6 (1993), 637-719. MR 93m:11043
28. M. Harris, L-functions of 2 × 2 unitary groups and factorization of periods of Hilbert modular forms, Jour. AMS 6 (1993), 637-719. MR 93m:11043
29. M. Harris, Non-vanishing of L-functions of 2 × 2 unitary groups. Forum Math. 5 (1993), 405-419. MR 94k:11057
30. M. Harris, Non-vanishing of L-functions of 2 × 2 unitary groups. Forum Math. 5 (1993), 405-419. MR 94k:11057
31. M. Harris and S. Kudla, The central critical value of a triple product L-function, Annals of Math. 133 (1991), 605-672. MR 93a:11043
32. M. Harris and S. Kudla, The central critical value of a triple product L-function, Annals of Math. 133 (1991), 605-672. MR 93a:11043
33. 2 duality for stable reductive dual pairs.
34. H. Jacquet, Principal L-functions of the linear group. Automorphic Forms. Representations and L-Functions, part 2, Proc. Symp. Pure Math., vol. 33. AMS, Providence. 1979, pp. 63-86. MR 81f:22029
35. H. Jacquet, Principal L-functions of the linear group. Automorphic Forms. Representations and L-Functions, part 2, Proc. Symp. Pure Math., vol. 33. AMS, Providence. 1979, pp. 63-86. MR 81f:22029
36. M. Karel, Values of certain Whittaker functions on p-adic groups, Ill. Jour. of Math. 26 (1983), 552-575. MR 84f:10033
37. M. Karel, Values of certain Whittaker functions on p-adic groups, Ill. Jour. of Math. 26 (1983), 552-575. MR 84f:10033
38. S. Kudla, On the local theta correspondence, Inventiones math. 83 (1986), 229-255. MR 87e:22037
39. S. Kudla, On the local theta correspondence, Inventiones math. 83 (1986), 229-255. MR 87e:22037
40. S. Kudla, Splitting metaplectic covers of dual reductive pairs. Israel J. Math. 87 (1994), 361-401. MR 95h:22019
41. S. Kudla, Splitting metaplectic covers of dual reductive pairs. Israel J. Math. 87 (1994), 361-401. MR 95h:22019
42. S. Kudla and S. Rallis, A regularized Siegel-Weil formula, the first term identity, Annals of Math. 140 (1994), 1-80. MR 95f:11036
43. S. Kudla and S. Rallis, A regularized Siegel-Weil formula, the first term identity, Annals of Math. 140 (1994), 1-80. MR 95f:11036
44. S. Kudla and S. Rallis, On first occurrence in the local theta correspondence, preprint, 1996.
45. S. Kudla and W. Sweet, Degenerate principal series for unitary groups, preprint (1994).
46. J.-P. Labesse and R. P. Langlands, L-indistinguishability for SL(2), Canad. J. Math. 31 (1979), 726-85. MR 81b:22017
47. J.-P. Labesse and R. P. Langlands, L-indistinguishability for SL(2), Canad. J. Math. 31 (1979), 726-85. MR 81b:22017
48. R. P. Langlands and D. Ramakrishnan, The description of the theorem. Zeta functions of Picard modular surfaces (R. P. Langlands and D. Ramakrishnan, eds.), Publications CRM, Montreal, 1992, pp. 255-301. MR 93d:11055
49. R. P. Langlands and D. Ramakrishnan, The description of the theorem. Zeta functions of Picard modular surfaces (R. P. Langlands and D. Ramakrishnan, eds.), Publications CRM, Montreal, 1992, pp. 255-301. MR 93d:11055
50. Jian-Shu Li, Non-vanishing theorems for the cohomology of certain arithmetic quotients, J. Reine Angew. Math. 428 (1992), 177-217. MR 93e:11067
51. Jian-Shu Li, Non-vanishing theorems for the cohomology of certain arithmetic quotients, J. Reine Angew. Math. 428 (1992), 177-217. MR 93e:11067
52. C. Moeglin, M.-F. Vigneras, and J.-L. Waldspurger, Correspondances de Howe sur un corp p-adiques, Lecture Notes in Math. 1291, Springer Verlag, New York, 1987. MR 91f:11040
53. C. Moeglin, M.-F. Vigneras, and J.-L. Waldspurger, Correspondances de Howe sur un corp p-adiques, Lecture Notes in Math. 1291, Springer Verlag, New York, 1987. MR 91f:11040
54. C. Moen, The dual pair (U(1), U(1)) over a p-adic field, Pacific J. Math. 158 (1993), 365-386. MR 94a:22036
55. C. Moen, The dual pair (U(1), U(1)) over a p-adic field, Pacific J. Math. 158 (1993), 365-386. MR 94a:22036
56. I. I. Piatetski-Shapiro and S. Rallis, L-functions for classical groups. Lecture Notes in Math. 1254, Springer Verlag, New York, 1987, pp. 1-52. MR 89b:11046
57. I. I. Piatetski-Shapiro and S. Rallis, L-functions for classical groups. Lecture Notes in Math. 1254, Springer Verlag, New York, 1987, pp. 1-52. MR 89b:11046
58. I. I. Piatetski-Shapiro and S. Rallis, e-factors of representations of classical groups, Proc. Symp. Nat. Acad. Sci. 83 (1986), 4589-4593. MR 88a:11053
59. I. I. Piatetski-Shapiro and S. Rallis, e-factors of representations of classical groups, Proc. Symp. Nat. Acad. Sci. 83 (1986), 4589-4593. MR 88a:11053
60. I. I. Piatetski-Shapiro and S. Rallis, Rankin triple L-functions, Compositio Math. 64 (1987), 31-115. MR 89k:11037
61. I. I. Piatetski-Shapiro and S. Rallis, Rankin triple L-functions, Compositio Math. 64 (1987), 31-115. MR 89k:11037
62. D. Prasad, Trilinear forms for representations of GL(2) and local e-factors, Compositio Math. 75 (1990), 1-46. MR 91i:22023
63. D. Prasad, Trilinear forms for representations of GL(2) and local e-factors, Compositio Math. 75 (1990), 1-46. MR 91i:22023
64. D. Prasad, On the local Howe duality correspondence, International Math. Res. Notices 11 (1993), 279-287. MR 94k:22036
65. D. Prasad, On the local Howe duality correspondence, International Math. Res. Notices 11 (1993), 279-287. MR 94k:22036
66. S. Rallis, On the Howe duality conjecture, Compositio Math. 51 (1984), 333-399. MR 85g:22034
67. S. Rallis, On the Howe duality conjecture, Compositio Math. 51 (1984), 333-399. MR 85g:22034
68. S. Rallis, Langlands functoriality and the Weil representation, Amer. J. Math. 104 (1982), 469-515. MR 84c:10025
69. S. Rallis, Langlands functoriality and the Weil representation, Amer. J. Math. 104 (1982), 469-515. MR 84c:10025
70. S. Rallis, Injectivity properties of liftings associated to Weil representations, Compositio Math. 52 (1984), 139-169. MR 86d:11038
71. S. Rallis, Injectivity properties of liftings associated to Weil representations, Compositio Math. 52 (1984), 139-169. MR 86d:11038
72. S. Rallis, Poles of standard L-functions, Proceedings of the International Congress of Mathematics, Kyoto, Springer Verlag, New York, 1990, pp. 833-845. MR 93f:11041
73. S. Rallis, Poles of standard L-functions, Proceedings of the International Congress of Mathematics, Kyoto, Springer Verlag, New York, 1990, pp. 833-845. MR 93f:11041
74. R. Ranga Rao, On some explicit formulas in the theory of Weil representation, Pacific J. of Math. 157 (1993), 335-371. MR 94a:22037
75. R. Ranga Rao, On some explicit formulas in the theory of Weil representation, Pacific J. of Math. 157 (1993), 335-371. MR 94a:22037
76. J. Rogawski, Automorphic representations of unitary groups in three variables, Annals of Math. Studies 123, Princeton University Press, Princeton, N.J., 1990. MR 91k:22037
77. J. Rogawski, Automorphic representations of unitary groups in three variables, Annals of Math. Studies 123, Princeton University Press, Princeton, N.J., 1990. MR 91k:22037
78. J. Rogawski, The multiplicity formula for A-packets, Zeta functions of Picard modular surfaces (R. P. Langlands and D. Ramakrishnan, eds.), Publications CRM, Montreal, 1992, pp. 395-419. MR 93f:11042
79. J. Rogawski, The multiplicity formula for A-packets, Zeta functions of Picard modular surfaces (R. P. Langlands and D. Ramakrishnan, eds.), Publications CRM, Montreal, 1992, pp. 395-419. MR 93f:11042
80. G. Shimura, On Eisenstein series, Duke Math. J. 50 (1983), 417-476. MR 84k:11019
81. G. Shimura, On Eisenstein series, Duke Math. J. 50 (1983), 417-476. MR 84k:11019
82. W. Sweet, A computation of the gamma matrix of a family of p-adic zeta integrals, preprint 1991.
83. J. Tate, Fourier analysis in number fields and Hecke's zeta function, Algebraic Number Theory (Cassels and Frohlich, ed.), Academic Press, 1968. MR 36:121
84. J. Tate, Fourier analysis in number fields and Hecke's zeta function, Algebraic Number Theory (Cassels and Frohlich, ed.), Academic Press, 1968. MR 36:121
85. J. Tate, Number theoretic background, Automorphic Forms, Representations and L-Functions, part 2, Proc. Symp. Pure Math., vol. 33, AMS. Providence, 1979, pp. 3-22. MR 80m:12009
86. J. Tate, Number theoretic background, Automorphic Forms, Representations and L-Functions, part 2, Proc. Symp. Pure Math., vol. 33, AMS. Providence, 1979, pp. 3-22. MR 80m:12009
87. 2, Amer. J. Math. 105 (1983), 1277-1308. MR 86a:22018
88. 2, Amer. J. Math. 105 (1983), 1277-1308. MR 86a:22018
89. D. Vogan, The local Langlands conjecture, Representation theory of groups and algebras, AMS. Contemporary Math. 145. Providence, R.I., 1993, pp. 305-379. MR 94e:22031
90. D. Vogan, The local Langlands conjecture, Representation theory of groups and algebras, AMS. Contemporary Math. 145. Providence, R.I., 1993, pp. 305-379. MR 94e:22031
91. J.-L. Waldspurger, Sur les valeurs de certains fonctions L automorphes en leur centre de symétrie, Compositio Math. 54 (1985), 173-242. MR 87g:11061b
92. J.-L. Waldspurger, Sur les valeurs de certains fonctions L automorphes en leur centre de symétrie, Compositio Math. 54 (1985), 173-242. MR 87g:11061b
93. J.-L. Waldspurger, Demonstration d'une conjecture de duality de Howe dans le case p-adiques, p ≠ 2, Festschrift in Honor of Piatetski-Shapiro, vol. 2, Israel Math. Conf. Proc., 1990, pp. 267-324. MR 93h:22035
94. J.-L. Waldspurger, Demonstration d'une conjecture de duality de Howe dans le case p-adiques, p ≠ 2, Festschrift in Honor of Piatetski-Shapiro, vol. 2, Israel Math. Conf. Proc., 1990, pp. 267-324. MR 93h:22035
95. J.-L. Waldspurger, Correspondance de Shimura et quaternions, Forum Math. 3 (1991), 219-307. MR 92g:11054
96. J.-L. Waldspurger, Correspondance de Shimura et quaternions, Forum Math. 3 (1991), 219-307. MR 92g:11054
97. Tonghai Yang, Theta liftings and L-functions of elliptic curves, Thesis, Univ. of Maryland (1995).