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Estimating Hecke eigenvalues of Siegel modular forms
W. Duke, R. Howe, and J.-S. Li
Source: Duke Math. J. Volume 67, Number 1
(1992), 219-240.
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077294276
Mathematical Reviews number (MathSciNet): MR1174607
Zentralblatt MATH identifier: 0766.11026
Digital Object Identifier: doi:10.1215/S0012-7094-92-06708-1
References
[A] A. N. Andrianov, Quadratic forms and Hecke operators, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 286, Springer-Verlag, Berlin, 1987.
Mathematical Reviews (MathSciNet): MR88g:11028
Zentralblatt MATH: 0613.10023
[BR] S. Böcherer and S. Raghavan, On Fourier coefficients of Siegel modular forms, J. Reine Angew. Math. 384 (1988), 80–101.
Mathematical Reviews (MathSciNet): MR89c:11068
Zentralblatt MATH: 0636.10022
[B] A. Borel, Automorphic $L$-functions, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 2 eds. A. Borel and W. Casselman, Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 27–61.
Mathematical Reviews (MathSciNet): MR81m:10056
Zentralblatt MATH: 0412.10017
[Bk] N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles, No. 1337, Hermann, Paris, 1968.
Mathematical Reviews (MathSciNet): MR39:1590
Zentralblatt MATH: 0186.33001
[C] W. Casselman, Introduction to the theory of admissible representations of $P$-adic reductive groups, preprint.
[CHH] M. Cowling, U. Haagerup, and R. Howe, Almost $L\sp 2$ matrix coefficients, J. Reine Angew. Math. 387 (1988), 97–110.
Mathematical Reviews (MathSciNet): MR89i:22008
Zentralblatt MATH: 0638.22004
[De] P. Deligne, La conjecture de Weil. I, Inst. Hautes Études Sci. Publ. Math. (1974), no. 43, 273–307.
Mathematical Reviews (MathSciNet): MR49:5013
Zentralblatt MATH: 0219.14006
Digital Object Identifier: doi:10.1007/BF02684373
[EZ] M. Eichler and D. Zagier, The theory of Jacobi forms, Progress in Mathematics, vol. 55, Birkhäuser Boston Inc., Boston, MA, 1985.
Mathematical Reviews (MathSciNet): MR86j:11043
Zentralblatt MATH: 0554.10018
[Fo] O. M. Fomenko, Fourier coefficients of Siegel cusp forms of genus $n$, J. Soviet Math. 38 (1987), 2148–2157.
Zentralblatt MATH: 0624.10022
[Fr] E. Freitag, Siegelsche Modulfunktionen, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 254, Springer-Verlag, Berlin, 1983.
Mathematical Reviews (MathSciNet): MR88b:11027
Zentralblatt MATH: 0498.10016
[G] S. S. Gelbart, Weil's representation and the spectrum of the metaplectic group, Springer-Verlag, Berlin, 1976.
Mathematical Reviews (MathSciNet): MR54:12654
Zentralblatt MATH: 0365.22017
[H1] R. Howe, On a notion of rank for unitary representations of the classical groups, Harmonic Analysis and Group Representations: C.I.M.E. II ciclo 1980, Palazzone della Scuola Normale Superiore Cortona-Arezzo, Liguori Editore, Naples, 1982, pp. 223–332.
Mathematical Reviews (MathSciNet): MR777342
[H2] R. Howe, Small unitary representations of classical groups, Group representations, ergodic theory, operator algebras, and mathematical physics (Berkeley, Calif., 1984) ed. C. Moore, Math. Sci. Res. Inst. Publ., vol. 6, Springer, New York, 1987, Proceedings of a Conference in Honor of G. W. Mackey, pp. 121–150.
Mathematical Reviews (MathSciNet): MR89e:22021
Zentralblatt MATH: 0635.22014
[H3] R. Howe, Automorphic forms of low rank, Noncommutative harmonic analysis and Lie groups (Marseille, 1980), Lecture Notes in Math., vol. 880, Springer, Berlin, 1981, pp. 211–248.
Mathematical Reviews (MathSciNet): MR83j:10033
Zentralblatt MATH: 0463.10015
[HPS] R. Howe and I. I. Piatetski-Shapiro, A counterexample to the “generalized Ramanujan conjecture” for (quasi-) split groups, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 1 eds. W. Casselman and A. Borel, Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 315–322.
Mathematical Reviews (MathSciNet): MR81f:22036
Zentralblatt MATH: 0423.22018
[I] N. Iwahori, Generalized Tits system (Bruhat decompostition) on $p$-adic semisimple groups, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965), Amer. Math. Soc., Providence, R.I., 1966, pp. 71–83.
Mathematical Reviews (MathSciNet): MR35:6693
Zentralblatt MATH: 0199.06901
[Ki] Y. Kitaoka, Fourier coefficients of Siegel cusp forms of degree two, Nagoya Math. J. 93 (1984), 149–171.
Mathematical Reviews (MathSciNet): MR85i:11046
Zentralblatt MATH: 0531.10031
Project Euclid: euclid.nmj/1118787433
[Kl] H. Klingen, Introductory lectures on Siegel modular forms, Cambridge Studies in Advanced Mathematics, vol. 20, Cambridge University Press, Cambridge, 1990.
Mathematical Reviews (MathSciNet): MR91a:11021
Zentralblatt MATH: 0693.10023
[Kn] M. Kneser, Strong approximation, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965), Amer. Math. Soc., Providence, R.I., 1966, pp. 187–196.
Mathematical Reviews (MathSciNet): MR35:4225
Zentralblatt MATH: 0201.37904
[Ko1] W. Kohnen, A simple remark on eigenvalues of Hecke operators on Siegel modular forms, Abh. Math. Sem. Univ. Hamburg 57 (1987), 33–35.
Mathematical Reviews (MathSciNet): MR89k:11035
Zentralblatt MATH: 0641.10022
Digital Object Identifier: doi:10.1007/BF02941597
[Ko2] W. Kohnen, A note on eigenvalues of Hecke operators on Siegel modular forms of degree two, preprint, 1990.
Mathematical Reviews (MathSciNet): MR1068125
Zentralblatt MATH: 0736.11025
Digital Object Identifier: doi:10.2307/2048596
JSTOR: links.jstor.org
[K] S. S. Kudla, On the local theta-correspondence, Invent. Math. 83 (1986), no. 2, 229–255.
Mathematical Reviews (MathSciNet): MR87e:22037
Zentralblatt MATH: 0583.22010
Digital Object Identifier: doi:10.1007/BF01388961
[Kur] N. Kurokawa, Examples of eigenvalues of Hecke operators on Siegel cusp forms of degree two, Invent. Math. 49 (1978), no. 2, 149–165.
Mathematical Reviews (MathSciNet): MR80b:10040
Zentralblatt MATH: 0397.10018
Digital Object Identifier: doi:10.1007/BF01403084
[L1] J. Li, Singular unitary representations of classical groups, Invent. Math. 97 (1989), no. 2, 237–255.
Mathematical Reviews (MathSciNet): MR90h:22021
Zentralblatt MATH: 0694.22011
Digital Object Identifier: doi:10.1007/BF01389041
[L2] J. Li, Nonexistence of singular cusp forms, to appear in Compositio Math.
Mathematical Reviews (MathSciNet): MR1168122
[M] H. Maass, Siegel's modular forms and Dirichlet series, Springer-Verlag, Berlin, 1971.
Mathematical Reviews (MathSciNet): MR49:8938
Zentralblatt MATH: 0224.10028
[Rag] S. Raghavan, Modular forms of degree $n$ and representation by quadratic forms, Ann. of Math. (2) 70 (1959), 446–477.
Mathematical Reviews (MathSciNet): MR23:A136
Zentralblatt MATH: 0093.08002
Digital Object Identifier: doi:10.2307/1970325
JSTOR: links.jstor.org
[R] S. Rallis, Langlands' functoriality and the Weil representation, Amer. J. Math. 104 (1982), no. 3, 469–515.
Mathematical Reviews (MathSciNet): MR84c:10025
Zentralblatt MATH: 0532.22016
Digital Object Identifier: doi:10.2307/2374151
JSTOR: links.jstor.org
[Ra] S. Ramanujan, On certain arithmetical functions, Trans. Cambridge Philos. Soc. 22 (1916), 159–184, Collected Papers, Cambridge Univ. Press, Cambridge, 1927, 136–162.
[Ro] F. Rodier, Sur les représentations non ramifiées des groupes réductifs $p$-adiques; l'exemple de $\rm GSp(4)$, Bull. Soc. Math. France 116 (1988), no. 1, 15–42.
Mathematical Reviews (MathSciNet): MR89i:22033
Zentralblatt MATH: 0662.22011
[Sa] I. Satake, Theory of spherical functions on reductive algebraic groups over $\germ p$-adic fields, Inst. Hautes Études Sci. Publ. Math. (1963), no. 18, 5–69.
Mathematical Reviews (MathSciNet): MR33:4059
Zentralblatt MATH: 0122.28501
Digital Object Identifier: doi:10.1007/BF02684781
[Sh] F. Shahidi, On the Ramanujan conjecture and finiteness of poles for certain $L$-functions, Ann. of Math. (2) 127 (1988), no. 3, 547–584.
Mathematical Reviews (MathSciNet): MR89h:11021
Zentralblatt MATH: 0654.10029
Digital Object Identifier: doi:10.2307/2007005
JSTOR: links.jstor.org
[Si] A. J. Silberger, The Langlands quotient theorem for $p$-adic groups, Math. Ann. 236 (1978), no. 2, 95–104.
Mathematical Reviews (MathSciNet): MR58:22413
Zentralblatt MATH: 0362.20029
Digital Object Identifier: doi:10.1007/BF01351383
[St] R. Steinberg, Lectures on Chevalley groups, Yale University, New Haven, Conn., 1968.
Mathematical Reviews (MathSciNet): MR57:6215
Zentralblatt MATH: 0307.22001
[We] A. Weil, Basic Number Theory, 3rd edition ed., Die Grundlehren der Mathematischen Wissenschaften, vol. 144, Springer-Verlag, New York, 1974.
Mathematical Reviews (MathSciNet): MR55:302
Zentralblatt MATH: 0326.12001
[W] R. Weissauer, Eisensteinreihen vom Gewicht $n+1$ zur Siegelschen Modulgruppe $n$-ten Grades, Math. Ann. 268 (1984), no. 3, 357–377.
Mathematical Reviews (MathSciNet): MR86h:11043
Zentralblatt MATH: 0524.10022
Digital Object Identifier: doi:10.1007/BF01457064
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