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Fourier-Jacobi expansions of Eisenstein series

Posted on:1990-06-02Degree:Ph.DType:Thesis
University:Brandeis UniversityCandidate:Johnson, JenniferFull Text:PDF
GTID:2470390017453418Subject:Mathematics
Abstract/Summary:PDF Full Text Request
This thesis concerns the computation of the Fourier coefficients of Eisenstein series for the symplectic group (in the holomorphic case). The main goal is to compute the Fourier coefficients of Eisenstein liftings of cusp forms on boundary components in terms of an Eisenstein series attached to a 0-dimensional boundary component and an L-function attached to the cuspidal representation to which f belongs.;The results obtained are valid for level one and for any totally number field. The computation in general is not complete. Formulas analagous to Bocherer's results before he applies Andrianov's results to get a product formula are obtained in general at the holomorphic point. Technical modifications of the work of Piatetski-Shapiro and Rallis should yield the final result. In a special case these computations yield a connection between special values of two different L-functions attached to the cusp form f. Again, technical modifications should yield a relation between these L-functions in general.;The arguments here are an adelic generalization of a classical argument given by S. Bocherer. Bocherer uses results of Andrianov to obtain his final formula. Computations by Piatetski-Shapiro and Rallis play an analagous role in the adelic treatment.
Keywords/Search Tags:Eisenstein
PDF Full Text Request
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