Geodesic
Interaction of Hecke--Shimura rings acting on theta-series
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 28, Tome 418 (2013), pp. 8-27

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The paper considers principal features of interactions (transfer homomorphisms) for Hecke–Shimura rings of integral symplectic groups and integral orthogonal groups of positive definite integral quadratic forms both operating on theta-series of positive definite quadratic forms by Hecke operators. 
@article{ZNSL_2013_418_a1,
     author = {A. Andrianov},
     title = {Interaction of {Hecke--Shimura} rings acting on theta-series},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {8--27},
     publisher = {mathdoc},
     volume = {418},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_418_a1/}
}
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A. Andrianov. Interaction of Hecke--Shimura rings acting on theta-series. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 28, Tome 418 (2013), pp. 8-27. http://geodesic.mathdoc.fr/item/ZNSL_2013_418_a1/