Geodesic
The Linnik conjecture.~II
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part VI, Tome 283 (2001), pp. 37-49

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The Linnik conjecture is proved in the measquare variant over the integer parameters $(m,n)$ of the Kloosterman sum $S(m,n;c)$. This mean may be called arithmetic, because the arithmetics of Kloosterman sums depends on the parameters $(m,n)$. 
@article{ZNSL_2001_283_a3,
     author = {A. I. Vinogradov},
     title = {The {Linnik} {conjecture.~II}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {37--49},
     publisher = {mathdoc},
     volume = {283},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_283_a3/}
}
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A. I. Vinogradov. The Linnik conjecture.~II. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part VI, Tome 283 (2001), pp. 37-49. http://geodesic.mathdoc.fr/item/ZNSL_2001_283_a3/