Arithmetic invariants and automorphic L-functions for automorphic forms of several variables

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We investigated arithmetic properties of Arakawa lifts, which are automorphic forms on the unitary group of degree two for a quaternion algebra over the rational number field constructed via theta lifting. In particular we obtained a formula for the square of the absolute value of a certain average of Fourier coefficients of an Arakawa lift in terms of special values of automorphic L-functions.We characterize the holomorphic Borcherds lifts on orthogonal groups of quadratic forms of signature (2, n+2) in terms of the multiplicative symmetries. We also showed that a similar fact holds for Jacobi forms.