Geodesic
The points beneath a hyperbola and the circle problem. A spectral approach
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 9, Tome 289 (2002), pp. 63-75

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This is the first introductory part of the paper in which a spectral idea is presented for the solution of the circle problem and the problem on the points beneath a hyperbola. In the second and third parts technical details of such a solution will be given. 
@article{ZNSL_2002_289_a3,
     author = {A. I. Vinogradov},
     title = {The points beneath a hyperbola and the circle problem. {A} spectral approach},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {63--75},
     publisher = {mathdoc},
     volume = {289},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_289_a3/}
}
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A. I. Vinogradov. The points beneath a hyperbola and the circle problem. A spectral approach. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 9, Tome 289 (2002), pp. 63-75. http://geodesic.mathdoc.fr/item/ZNSL_2002_289_a3/