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 $G=SL_2(\mathbf Z)$, $\chi=1$.