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D. Bump, D. Ginzburg, J. Hoffstein (1996)
The symmetric cubeInventiones mathematicae, 125
D. Bump, D. Ginzburg (1992)
Symmetric square L-functions on GL(r)Annals of Mathematics, 136
D. Ginzburg (1995)
On the symmetric fourth powerL-function of GL2Israel Journal of Mathematics, 92
M. Harris, S. Kudla (1991)
The central critical value of the triple product $L$-functionAnnals of Mathematics, 133
J. Arthur (1978)
A trace formula for reductive groups I terms associated to classes in $G(\mathbf{Q})$Duke Mathematical Journal, 45
G. Shimura (1975)
On the Holomorphy of Certain Dirichlet SeriesProceedings of The London Mathematical Society
D. Ginzburg, S. Rallis, D. Soudry (1997)
Cubic correspondences arising from G2American Journal of Mathematics, 119
T. Matsuzawa (1971)
Sur une classe d'équations paraboliques dégénéréesAnnales Scientifiques De L Ecole Normale Superieure, 4
Dihua Jiang (1998)
Nonvanishing of the Central Critical Value of the Triple Product L-FunctionsInternational Mathematics Research Notices, 1998
S. Gelbart, Hervé Jacquet (1978)
A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$Annales Scientifiques De L Ecole Normale Superieure, 11
D. Ginzburg, S. Rallis, D. Soudry (1999)
On explicit lifts of cusp forms from GLm to classical groupsAnnals of Mathematics, 150
Henry Kim, F. Shahidi (1999)
Symmetric cube L-functions for GL_2 are entirearXiv: Number Theory
B. Gross, Dipendra Prasad (1992)
On the Decomposition of a Representation of SOn When Restricted to SOn-1Canadian Journal of Mathematics, 44
Dihua Jiang, Zhengyu Mao, S. Rallis (1999)
A relative Kuznietsov trace formula on G2manuscripta mathematica, 99
Dihua Jiang (1998)
G2-periods and residual representationsCrelle's Journal, 497
D. Ginzburg, Dihua Jiang (2000)
A Siegel–Weil Identity for G2 and Poles of L-Functions☆Journal of Number Theory, 82
S. Kudla, S. Rallis (1994)
A Regularized Siegel-Weil Formula: The First Term IdentityAnnals of Mathematics, 140
F. Shahidi (1994)
Symmetric power -functions for (2)
S. Patterson, I. Piatetski-Shapiro (1989)
The symmetric-squareL-function attached to a cuspidal automorphic representation ofGL3Mathematische Annalen, 283
F. Shahidi (1989)
Third symmetric power $L$-functions for $GL(2)$Compositio Mathematica, 70
Abstract. In this paper we characterize the nonvanishing of the central critical value of the third symmetric power L-functions of irreducible cuspidal automorphic representations p of GL2 A in terms of the occurrence of p in the spectral decomposition of the tensor product of two automorphic theta representations on the cubic cover of GL2 A, which was constructed by Kazhdan and Patterson in [KP]. 1991 Mathematics Subject Classi®cation: 11F, 22E. 1 Introduction Let p be an irreducible cuspidal automorphic representation of GL2 A and n be a positive integer. One can de®ne, following Langlands, the n-th symmetric power L-function LsY pY Sym n . For the signi®cance of this family of automorphic L-functions, we refer to [Sh], for instance. The symmetric cube L-function, LsY pY Sym 3 , was ®rst studied by F. Shahidi in [Sh1] using the Langlands-Shahidi method to establish the analytic properties as conjectured by Langlands (meromorphic continuation and functional equation, . . .). In a recent work of D. Bump, D. Ginzburg and J. Ho¨stein [BGH], an integral representation was found for the symmetric cube L-functions, by which they can prove that the partial symmetric cube L-function is holomorphic for Res b 3 except
Forum Mathematicum – de Gruyter
Published: Jan 5, 2001
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