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Starting from a Hilbert cusp form of weight 2κ, we will construct a Hilbert-Siegel cusp form of weight κ + m 2 and degree m and its transfer to inner forms of symplectic groups. Applications include a relation between Fourier coefficients of Hilbert cusp forms of weight n + 1 2 and a certain weighted sum of the representation numbers of a quadratic form of rank 2n by a quadratic form of rank 4n.doi:10.2307/3062143 fatcat:ghowgbl3r5d4ppn6aj4mehf7xq