Geodesic
Summation formulas for general Kloosterman sums
Zapiski Nauchnykh Seminarov POMI, Studies in number theory. Part 5, Tome 82 (1979), pp. 103-135

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N. V. Kuznetsov's summation formula is generalized to the case of a discrete subgroup $G\subset SL_2(\mathbf R)$ and a system of multiplicators $\chi$, satisfying certain not too restrictive conditions. In the arithmetic cases, when $G$ is a congruence-subgroup in $SL_2(\mathbf Z)$, these conditions are satisfied. N. V. Kuznetsov's formula has been proved for the case $G=SL_2(\mathbf Z)$, $\chi=1$. 
@article{ZNSL_1979_82_a6,
     author = {N. V. Proskurin},
     title = {Summation formulas for general {Kloosterman} sums},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {103--135},
     publisher = {mathdoc},
     volume = {82},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_82_a6/}
}
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N. V. Proskurin. Summation formulas for general Kloosterman sums. Zapiski Nauchnykh Seminarov POMI, Studies in number theory. Part 5, Tome 82 (1979), pp. 103-135. http://geodesic.mathdoc.fr/item/ZNSL_1979_82_a6/