Geodesic
Jacobi functions and Euler products for Hermitian modular forms
Zapiski Nauchnykh Seminarov POMI, Modular functions and quadratic forms. Part 1, Tome 183 (1990), pp. 77-123

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One defines different types of Hecke operators on the spaces of Jacobi modular forms. For modular forms of genus two it is established that non-standard zeta-function $Z_p^{(2)}(s)$ with degree six of local factors is equal to the Dirichlet series constructed from the Fourier-Jacobi coefficients of eigeafunctions $F$. It is proved that $Z_p^{(2)}(s)$ can be continued analytically into the entire complex plane. 
@article{ZNSL_1990_183_a4,
     author = {V. A. Gritsenko},
     title = {Jacobi functions and {Euler} products for {Hermitian} modular forms},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {77--123},
     publisher = {mathdoc},
     volume = {183},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1990_183_a4/}
}
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V. A. Gritsenko. Jacobi functions and Euler products for Hermitian modular forms. Zapiski Nauchnykh Seminarov POMI, Modular functions and quadratic forms. Part 1, Tome 183 (1990), pp. 77-123. http://geodesic.mathdoc.fr/item/ZNSL_1990_183_a4/