We define generalized Mellin transforms of mixed cusp forms, show their convergence, and prove that the function obtained by such a Mellin transform of a mixed cusp form satisfies a certain functional equation. We also prove that a mixed cusp form can be identified with a holomorphic form of the highest degree on an elliptic variety.

MSC Classifications:

11F12, 11F66, 11M06, 14K05 show english descriptions Automorphic forms, one variable
Langlands $L$-functions; one variable Dirichlet series and functional equations
$\zeta (s)$ and $L(s, \chi)$
Algebraic theory 11F12 - Automorphic forms, one variable
11F66 - Langlands $L$-functions; one variable Dirichlet series and functional equations
11M06 - $\zeta (s)$ and $L(s, \chi)$
14K05 - Algebraic theory

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