Mixed Hodge structures and automorphic forms for Siegel modular varieties of degree two.

Takayuki Oda; Joachim Schwermer

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Mixed automorphic forms generalize elliptic modular forms, and they occur naturally as holomorphic forms of the highest degree on families of abelian varieties parametrized by a Riemann surface. We construct generalized Eisenstein series and Poincaré series, and prove that they are mixed automorphic forms.