previous ::
next
Fourier coefficients of modular forms on G2
Wee Teck Gan, Benedict Gross, and Gordan Savin
Source: Duke Math. J. Volume 115, Number 1 (2002), 105-169.
Abstract
We develop a theory of Fourier coefficients for modular forms on the split exceptional group G2 over ℚ.
Primary Subjects: 11F30
Secondary Subjects: 11F55
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1085598120
Digital Object Identifier: doi:10.1215/S0012-7094-02-11514-2
Mathematical Reviews number (MathSciNet):
MR1932327
Zentralblatt MATH identifier:
01869850
References
H. Azad, M. Barry, and G. Seitz, On the structure of parabolic subgroups, Comm. Algebra 18 (1990), 551--562.
Mathematical Reviews (MathSciNet):
MR91d:20048
Digital Object Identifier: doi:10.1080/00927879008823931
A. Borel, Linear Algebraic Groups, 2d ed., Grad. Texts in Math. 126, Springer, New York, 1991.
Mathematical Reviews (MathSciNet):
MR92d:20001
A. Borel and H. Jacquet, ``Automorphic forms and automorphic representations'' in Atomorphic Forms, Representations and $L$-Functions (Corvallis, Ore., 1977), Part 1, Proc. Sympos. Pure Math. 33, Amer. Math. Soc., Providence, 1979 189--207.
Mathematical Reviews (MathSciNet):
MR81m:10055
A. Borel and J. Tits, Groupes réductifs, Inst. Hautes Études Sci. Publ. Math. 27 (1965), 55--150.
Mathematical Reviews (MathSciNet):
MR34:7527
Digital Object Identifier: doi:10.1007/BF02684375
N. Bourbaki, Éléments de mathématiques, fasc. 37: Groupes et algèbres de Lie, chapitres II, III, Actualités Sci. Indust. 1349, Hermann, Paris, 1972.
Mathematical Reviews (MathSciNet):
MR58:28083a
W. Casselman, Canonical extensions of Harish-Chandra modules to representations of $G$, Canad. J. Math. 41 (1989), 385--438.
Mathematical Reviews (MathSciNet):
MR90j:22013
H. Cohen, Sums involving the values at negative integers of $L$-functions of quadratic characters, Math. Ann. 217 (1975), 271--285.
Mathematical Reviews (MathSciNet):
MR52:3080
Digital Object Identifier: doi:10.1007/BF01436180
B. N. Delone and D. K. Faddeev, The Theory of Irrationalities of the Third Degree, Trans. Math. Monogr. 10, Amer. Math. Soc., Providence, 1964.
Mathematical Reviews (MathSciNet):
MR28:3955
M. Demazure, ``Sous-groupes paraboliques des groupes réductifs'' in Schémas en groupes, III, Séminaire de Géométrie Algébrique du Bois-Marie (SGA 3), Lecture Notes in Math. 153, Springer, New York, 1970, 426--517.
Mathematical Reviews (MathSciNet):
MR36:1451
W. T. Gan, An automorphic theta module for quaternionic exceptional groups, Canad. J. Math. 52 (2000), 737--756.
Mathematical Reviews (MathSciNet):
MR2001g:11074
--. --. --. --., A Siegel-Weil formula for exceptional groups, J. Reine Angew. Math. 528 (2000), 149--181.
Mathematical Reviews (MathSciNet):
MR2001k:11089
Digital Object Identifier: doi:10.1515/crll.2000.088
B. H. Gross, Groups over $\mathbbZ$, Invent. Math. 124 (1996), 263--279.
Mathematical Reviews (MathSciNet):
MR96m:20075
Digital Object Identifier: doi:10.1007/s002220050053
B. H. Gross, ``On the Satake isomorphism'' in Galois Representations in Arithmetic Algebraic Geometry (Durham, England, 1996), London Math. Soc. Lecture Note Ser. 254, Cambridge Univ. Press, Cambridge, 1998, 223--237.
Mathematical Reviews (MathSciNet):
MR2000e:22008
B. H. Gross and W. T. Gan, Commutative subrings of certain non-associative rings, Math. Ann. 314 (1999), 265--283.
Mathematical Reviews (MathSciNet):
MR2000j:11050
Digital Object Identifier: doi:10.1007/s002080050294
B. H. Gross and N. R. Wallach, On quaternionic discrete series representations, and their continuations, J. Reine Angew. Math. 481 (1996), 73--123.
Mathematical Reviews (MathSciNet):
MR98f:22022
J. W. Hoffman and J. Morales, Arithmetic of binary cubic forms, Enseign. Math. (2) 46 (2000), 61--94.
Mathematical Reviews (MathSciNet):
MR2001h:11048
J. S. Huang, P. Pandžić, and G. Savin, New dual pair correspondences, Duke Math. J. 82 (1996), 447--471.
Mathematical Reviews (MathSciNet):
MR97c:22015
Digital Object Identifier: doi:10.1215/S0012-7094-96-08220-4
Project Euclid: euclid.dmj/1077245041
D. H. Jiang and S. Rallis, Fourier coefficients of Eisenstein series of the exceptional group of type $G_2$, Pacific J. Math. 181 (1997), 281--314.
Mathematical Reviews (MathSciNet):
MR99d:11054
R. A. Rankin, Modular Forms and Functions, Cambridge Univ. Press, Cambridge, 1977.
Mathematical Reviews (MathSciNet):
MR58:16518
J.-P. Serre, A Course in Arithmetic, Grad. Texts in Math. 7, Springer, New York, 1973.
Mathematical Reviews (MathSciNet):
MR49:8956
--. --. --. --., Exemples de plongements des groupes $\PSL_2(\mathbbF_p)$ dans les groupes de Lie simples, Invent. Math. 124 (1996), 525--562.
Mathematical Reviews (MathSciNet):
MR97d:20056
Digital Object Identifier: doi:10.1007/s002220050062
T. A. Springer, Linear Algebraic Groups, 2d ed., Progr. Math. 9, Birkhäuser, Boston, 1998.
Mathematical Reviews (MathSciNet):
MR99h:20075
D. Vogan, The unitary dual of $G_2$, Invent. Math. 116 (1994), 677--791.
Mathematical Reviews (MathSciNet):
MR95b:22037
Digital Object Identifier: doi:10.1007/BF01231578
N. R. Wallach, Real Reductive Groups, II, Pure Appl. Math. 132, Vol. II, Academic Press, Boston, 1992.
Mathematical Reviews (MathSciNet):
MR93m:22018
--. --. --. --., ``$C^\infty$ vectors'' in Representations of Lie Groups and Quantum Groups (Trento, Italy, 1993), Pitman Res. Notes Math. Ser. 311, Longman Sci. Tech, Harlow, 1994, 205--270.
Mathematical Reviews (MathSciNet):
MR98g:22008
--------, Generalized Whittaker vectors for holomorphic and quaternionic representations, preprint, 2000, http://math.ucsd.edu/~nwallach/preprints.html
previous ::
next
Duke Mathematical Journal
