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Browsing by Author "Shen, Xin"

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    Unramified computation of tensor L-functions on symplectic groups
    (2013-06) Shen, Xin
    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.