On Metaplectic Forms of Classical Groups

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(1) We established a relation between Dirichlet series obtained as Fourier coefficients of metaplectic Eisenstein series and Rankin-Selberg convolutions of metaplectic forms.(2) Unramified distinguished representations were determined and their Whittaker functins were explicitely given in some case. It was shown that the Rankin-Selberg convolutions of metaplectic forms against ditinguished metaplectic forms have Euler product. We propose a conjecture that auto-morphic distinguished representations on a n-fold metaplectic group of GL(nr) are parametrized by automorphic cuspidal representations of GL(r).(3) We give a explicite formula for the dimension of Whittaker functionals on supercuspidal representations of metaplectic groups over a local field. Hence distinguished supercuspidal representations of metaplectic groups were determined.(4) We proved the existence of a maximal compact subring of a local field with respect to 1-lilbert symbol. Hence it follows the existence of an open compact subgroup of a metaplectic group over a local field, which has very good properties.