Geodesic
Certain analogues of the Hardy–Litlewood problem and density methods
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 4, Tome 112 (1981), pp. 121-142
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Applying density methods of the theory of the Dirichlet $L$-functions, one finds an asymptotic formula for the number of solutions of the equations of the type $N=\varphi(x,y)+m$ and $N=m-\varphi(x,y)$, where $\varphi(x,y)$ is a positive primitive quadratic form, while $m$ is representable by a sum of two squares and runs through its values without repetition. 
@article{ZNSL_1981_112_a9,
     author = {F. B. Koval'chik},
     title = {Certain analogues of the {Hardy{\textendash}Litlewood} problem and density methods},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {121--142},
     year = {1981},
     volume = {112},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_112_a9/}
}
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VL  - 112
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%A F. B. Koval'chik
%T Certain analogues of the Hardy–Litlewood problem and density methods
%J Zapiski Nauchnykh Seminarov POMI
%D 1981
%P 121-142
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%U http://geodesic.mathdoc.fr/item/ZNSL_1981_112_a9/
%G ru
%F ZNSL_1981_112_a9
F. B. Koval'chik. Certain analogues of the Hardy–Litlewood problem and density methods. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 4, Tome 112 (1981), pp. 121-142. http://geodesic.mathdoc.fr/item/ZNSL_1981_112_a9/