Journal ArticleDOI
On Fourier coefficients of automorphic forms of symplectic groups
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In this paper, it was shown that every cuspidal representation has a nontrivial Fourier coefficient with respect to a certain type of unipotent class, i.e., the class of symplectic groups.Abstract:
In this paper we study certain properties of Fourier coefficients of cuspidal representations on symplectic groups. We prove that every cuspidal representation has a nontrivial Fourier coefficient with respect to a certain type of unipotent class.read more
Citations
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Journal ArticleDOI
Certain conjectures relating unipotent orbits to automorphic representations
TL;DR: In this article, the structure of unipotent orbits is related to automorphic representations, and certain conjectures about the relation between these two structures are formulated and proved. But these conjectures do not consider the structure in terms of a set of automata.
Journal ArticleDOI
On the nonvanishing of the central value of the Rankin-Selberg L-functions
TL;DR: In this article, the Journal of the American Mathematical Society (JAMS) volume 17, issue 3, is devoted to a survey of the state-of-the-art work in the field of algebraic geometry.
MonographDOI
Eisenstein series and automorphic representations
TL;DR: In this article, the authors provide an introduction to the theory of Eisenstein series and automorphic forms on real simple Lie groups G, emphasising the role of representation theory.
Journal ArticleDOI
On fourier coefficients of automorphic forms of GL(n)
Dihua Jiang,Baiying Liu +1 more
TL;DR: In this paper, the Fourier expansion of the cuspidal automorphic form in terms of its Whittaker-Fourier coefficients is extended to the whole discrete spectrum of the space of all square-integrable automomorphic forms of GLn(A).
Journal ArticleDOI
On the genericity of cuspidal automorphic forms of SO2n+1
Dihua Jiang,David Soudry +1 more
TL;DR: In this article, the CAP conjecture for irreducible cuspidal automoprhic representations of SO2n+1(A) with special Bessel models was shown to hold for the special case of SO 2n + 1(A).
References
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Book
Nilpotent Orbits In Semisimple Lie Algebra: An Introduction
TL;DR: In this paper, the authors collected together the important results concerning the classification and properties of nilpotent orbits, beginning from the common ground of basic structure theory and concluded with a survey of advanced topics related to the above circle of ideas.
Journal ArticleDOI
On explicit lifts of cusp forms from GLm to classical groups
Journal ArticleDOI
Front d'onde des représentations des groupes classiques p-adiques
TL;DR: In this article, the definition algebrique du front d'onde d'une representation lisse d'un groupe p -adique, donnee par Kawanaka, was rappelle.
Journal ArticleDOI
Admissible nilpotent coadjoint orbits of p-adic reductive Lie groups
TL;DR: In this paper, the authors define admissibility for nilpotent coadjoint orbits of p-adic reductive Lie groups, and compute the set of admissible orbits for a range of examples.