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 
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/
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     author = {A. N. Andrianov},
     title = {On integration of modular forms with theta-series},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--21},
     year = {1990},
     volume = {183},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1990_183_a0/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.