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# Mellin Transforms of Mixed Cusp Forms

Published:1999-09-01
Printed: Sep 1999
• Youngju Choie
• Min Ho Lee
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## Abstract

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 - 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