Geodesic
On distribution of the integral $2\times2$ matrices
Zapiski Nauchnykh Seminarov POMI, Modular functions and quadratic forms. Part 1, Tome 183 (1990), pp. 49-55

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The integral solutions of equation $ad-bc=n$ in terms of spectral data of the automorphic Laplacian are investigated. Well-known results are improved in some cases. It is observed that general case can be treated by the same method. 
@article{ZNSL_1990_183_a2,
     author = {E. P. Golubeva},
     title = {On distribution of the integral $2\times2$ matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {49--55},
     publisher = {mathdoc},
     volume = {183},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1990_183_a2/}
}
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E. P. Golubeva. On distribution of the integral $2\times2$ matrices. Zapiski Nauchnykh Seminarov POMI, Modular functions and quadratic forms. Part 1, Tome 183 (1990), pp. 49-55. http://geodesic.mathdoc.fr/item/ZNSL_1990_183_a2/