Geodesic
On integration of modular forms with theta-series
Zapiski Nauchnykh Seminarov POMI, Modular functions and quadratic forms. Part 1, Tome 183 (1990), pp. 5-21

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Dirichlet series with analytical continuation and functional equation are obtained by means of Rankin-type integration of elliptic modular forms with theta-series of integral quadratic forms of determinant $\pm1$. In some cases the Dirichlet series are Mellin-transforms of elliptic modular forms of bigger weight. 
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     author = {A. N. Andrianov},
     title = {On integration of modular forms with theta-series},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     volume = {183},
     year = {1990},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_1990_183_a0/}
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A. N. Andrianov. On integration of modular forms with theta-series. Zapiski Nauchnykh Seminarov POMI, Modular functions and quadratic forms. Part 1, Tome 183 (1990), pp. 5-21. http://geodesic.mathdoc.fr/item/ZNSL_1990_183_a0/