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Some applications of Gelfand pairs to number theory
Author(s):
Benedict H.
Gross
Journal:
Bull. Amer. Math. Soc.
24
(1991),
277-301.
MSC (1985):
Primary 20C15, 11F66, 11F67
MathSciNet review:
1074028
Retrieve article in:
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References:
- [B] J. N. Bernstein, P-invariant distributions on GLn and the classification of unitary representations of GLn, Lecture Notes in Math., vol. 1041, Springer-Verlag, Berlin and New York, 1983.
- [B-L] L. C. Biedenharn and J-D. Louck, Angular momentum in quantum physics, Encyclopedia Math. Appl., vol. 8, 1981. MR 635121
- [Bo] N. Bourbaki, Groupes et algèbres de Lie, Chapitres VII-VIII, Hermann, Paris, 1975. MR 453824
- [C] P. Cartier, Representations of p-adic groups, Proc. Sympos. Pure Math., vol. 33, Amer. Math. Soc. Providence, RI, 1979, pp. 111-155. MR 546593
- [Di] P. Diaconis, Group representations in probability and statistics, Lecture Notes 11, Institute of Mathematical Statistics, Hayward, CA, 1988. MR 964069
- [D] J. Dieudonné, Special functions and linear representations of Lie groups, CBMS Regional Conf. Ser., vol. 42, 1980. MR 557540
- [G] P. Garrett, Decomposition of Eisenstein series: Rankin triple products, Ann. of Math. (2) 125 (1987), 209-235. MR 881269
- [G-V] R. Gangolli and V. S. Varadarajan, Harmonic analysis of spherical functions on real reductive groups, Ergeb. Math. Grenzgeb. vol. 101, Springer-Verlag, Berlin and New York, 1980. MR 954385
- [Ge] I. M. Gelfand, Spherical functions on symmetric spaces, Dokl. Akad. Nauk SSSR 70 (1950), 5-8. MR 33832
- [Ge-K] I. M. Gelfand and D. A. Kazhdan, Representations of GLn(K), Lie Groups and Their Representations, Halstead Press, 1975. MR 369612
- [Gr-K] B. H. Gross and S. Kudla, Heights and the central critical values of triple product L-functions, preprint, 1990. MR 1145805
- [Gr-P] B. H. Gross and D. Prasad, Test vectors for linear forms, Preprint, 1990. MR 1129372
- [H] S. Helgason, Differential geometry, Lie groups, and symmetric spaces, Academic Press, New York, 1978. MR 514561
- [H-K] M. Harris and S. Kudla, The central critical value of a triple product L-functions, preprint, 1989. MR 1109355
- [Jl] H. Jacquet, Automorphic forms on GL2, Lecture Notes in Math., vol. 278, Springer-Verlag, Berlin and New York, 1972. MR 562503
- [J2] H. Jacquet, Sur un résultat de Waldspurger, Ann. Sci. École Norm. Sup. (Pisa) 19 (1986), 185-229. MR 868299
- [J3] H. Jacquet, Sur un résultat de Waldspurger. II, Compositio Math. 63 (1987), 185-229. MR 909385
- [J4] H. Jacquet, On the nonvanishing of some L-functions, Proc. Indian Acad. Sci. 97 (1987), 117-155. MR 983610
- [J5] H. Jacquet and K. F. Lai, A relative trace formula, Compositio. Math. 54 (1985), 243-310. MR 783512
- [J-L] H. Jacquet and R. P. Langlands, Automorphic forms on GL2, Lecture Notes in Math., vol. 114, Springer-Verlag, Berlin and New York, 1970. MR 401654
- [K-V] B. Kimelfield and E. Vinberg, Homogeneous domains in flag manifolds and spherical subgroups of semisimple Lie groups, J. Funct. Anal. Appl. 12 (1978), 168-174.
- [K] M. Krämer, Sphärische Untergruppen in Kompakten zusammenhängenden Lie Gruppen, Compositio. Math. 38 (1979), 129-153. MR 528837
- [L] S. Lang, SL2(R), Addison-Wesley, Reading, MA, 1975. MR 430163
- [M] G. Mackey, Multiplicity free representations of finite groups, Pacific J. Math. 8 (1958), 503-510. MR 100035
- [M-O] J-F. Mestre and J. Oesterlé, Elliptic curves of prime conductor (in preparation).
- [PS-R] I. Piatetski-Shapiro and S. Rallis, Rankin triple L-functions, Compositio Math. 64(1987), 31-115. MR 911357
- [P] D. Prasad, Trilinear forms for GL2 of a local field and ε-factors, Compositio Math., vol. 75, no. 1, 1990, pp. 1-46.
- [S] J.-P. Serre, Trees, Springer-Verlag, Berlin and New York, 1980. MR 607504
- [Sp] T. A. Springer, Reductive groups, Automorphic Forms, Representations, and L-functions, Proc. Sympos. Pure Math., vol. 33, Amer. Math. Soc., Providence, RI, 1979, pp. 3-27. MR 546587
- [Ta] J. T. Tate, Number theoretic background, Proc. Sympos. Pure Math., vol. 33, Amer. Math. Soc. Providence, RI, 1979, pp. 3-26. MR 546607
- [T] J. Tunnell, Local ε-factors and characters of GL2, Amer. J. Math. 105 (1983), 1277-1308.
- [V] M.-F. Vigneras, Arithmétique des algèbres de quaternions, Lecture Notes in Math., vol. 800, Springer-Verlag, Berlin and New York, 1980. MR 580949
- [W] J.-L. Waldspurger, Sur les valeurs de certaines fonctions L automorphes en leur centre de symétrie, Compositio Math. 54 (1985), 173-242. MR 783511
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Additional Information:
DOI:
10.1090/S0273-0979-1991-16017-9
PII:
S 0273-0979(1991)16017-9
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