Geodesic
Power-moments of SL$_3(\mathbb Z)$ Kloosterman sums
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 3, pp. 833-845
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Classical Kloosterman sums have a prominent role in the study of automorphic forms on GL$_2$ and further they have numerous applications in analytic number theory. In recent years, various problems in analytic theory of automorphic forms on GL$_3$ have been considered, in which analogous GL$_3$-Kloosterman sums (related to the corresponding Bruhat decomposition) appear. In this note we investigate the first four power-moments of the Kloosterman sums associated with the group SL$_3(\mathbb Z)$. We give formulas for the first three moments and a nontrivial bound for the fourth.
Classical Kloosterman sums have a prominent role in the study of automorphic forms on GL$_2$ and further they have numerous applications in analytic number theory. In recent years, various problems in analytic theory of automorphic forms on GL$_3$ have been considered, in which analogous GL$_3$-Kloosterman sums (related to the corresponding Bruhat decomposition) appear. In this note we investigate the first four power-moments of the Kloosterman sums associated with the group SL$_3(\mathbb Z)$. We give formulas for the first three moments and a nontrivial bound for the fourth.
DOI : 10.1007/s10587-013-0056-7
Classification : 11L05, 11T23
Keywords: power-moment; SL$_3(\mathbb Z)$-Kloosterman sum 
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Djanković, Goran. Power-moments of SL$_3(\mathbb Z)$ Kloosterman sums. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 3, pp. 833-845. doi: 10.1007/s10587-013-0056-7

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