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1. Shen, Xin. Unramified computation of tensor L-functions on symplectic groups.

Degree: 2013, University of Minnesota

Tensor L-function is one of the important cases in the Langlands conjecture on the analytic properties of L-functions. Using the method of Rankin-Selberg convolution, Ginzburg, Jiang, Rallis and Soudry found an integral representation of the tensor L-functions for symplectic groups with non-generic representations. In this thesis we calculated the local integrals at the unramified places. First we gave a formula for the Whittaker-Shintani functions for symplectic groups, which is a generalization of the Casselman-Shalika formula for the Whittaker function in the generic case. Then we applied our formula and carried out the unramified calculation. We also investigated the local integrals at the non-archimedean, possibly ramified places and obtain some basic properties, such as convergence, rationalities, and non-vanishing of the local integrals for any given complex numbers.

Subjects/Keywords: Fourier-Jacobi model; L-function; Non-generic; Symplectic group; Umramified; Whittaker-Shintani function

…models used in the generic case is replaced by the Fourier-Jacobi model, which is a pairing… …Ginzburg, Jiang, Rallis and Soudry used the Fourier-Jacobi models to construct integrals for the… …of symplectic groups using Fourier-Jacobi models as introduced in [15]. Let F be… …can define the r-th Fourier Jacobi coefficient of ϕπ ∈ π as φ FJ ψV n (ϕπ )(… …satisfied, we call FJ ψV n (ϕπ )(h) the top Fourier-Jacobi coefficient r 14… 

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APA (6th Edition):

Shen, X. (2013). Unramified computation of tensor L-functions on symplectic groups. (Thesis). University of Minnesota. Retrieved from http://purl.umn.edu/156231

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Shen, Xin. “Unramified computation of tensor L-functions on symplectic groups.” 2013. Thesis, University of Minnesota. Accessed August 05, 2020. http://purl.umn.edu/156231.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Shen, Xin. “Unramified computation of tensor L-functions on symplectic groups.” 2013. Web. 05 Aug 2020.

Vancouver:

Shen X. Unramified computation of tensor L-functions on symplectic groups. [Internet] [Thesis]. University of Minnesota; 2013. [cited 2020 Aug 05]. Available from: http://purl.umn.edu/156231.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Shen X. Unramified computation of tensor L-functions on symplectic groups. [Thesis]. University of Minnesota; 2013. Available from: http://purl.umn.edu/156231

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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