Geodesic
Asymptotic distribution of $n$-th-order integral matrices belonging to a given residue class
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 4, Tome 112 (1981), pp. 85-111 Cet article a éte moissonné depuis la source Math-Net.Ru

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One obtains an asymptotic formula for the number of $n$-th-order integral matrices which belongs to a given domain of the discriminant surface and to a given residue class. 
@article{ZNSL_1981_112_a7,
     author = {A. M. Istamov},
     title = {Asymptotic distribution of $n$-th-order integral matrices belonging to a~given residue class},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {85--111},
     year = {1981},
     volume = {112},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_112_a7/}
}
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A. M. Istamov. Asymptotic distribution of $n$-th-order integral matrices belonging to a given residue class. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 4, Tome 112 (1981), pp. 85-111. http://geodesic.mathdoc.fr/item/ZNSL_1981_112_a7/