Geodesic
An identity involving Dedekind sums and generalized Kloosterman sums
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 4, pp. 991-1001
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The various properties of classical Dedekind sums $S(h, q)$ have been investigated by many authors. For example, Yanni Liu and Wenpeng Zhang: A hybrid mean value related to the Dedekind sums and Kloosterman sums, Acta Mathematica Sinica, 27 (2011), 435–440 studied the hybrid mean value properties involving Dedekind sums and generalized Kloosterman sums $K(m, n, r; q)$. The main purpose of this paper, is using the analytic methods and the properties of character sums, to study the computational problem of one kind of hybrid mean value involving Dedekind sums and generalized Kloosterman sums, and give an interesting identity.
The various properties of classical Dedekind sums $S(h, q)$ have been investigated by many authors. For example, Yanni Liu and Wenpeng Zhang: A hybrid mean value related to the Dedekind sums and Kloosterman sums, Acta Mathematica Sinica, 27 (2011), 435–440 studied the hybrid mean value properties involving Dedekind sums and generalized Kloosterman sums $K(m, n, r; q)$. The main purpose of this paper, is using the analytic methods and the properties of character sums, to study the computational problem of one kind of hybrid mean value involving Dedekind sums and generalized Kloosterman sums, and give an interesting identity.
DOI : 10.1007/s10587-012-0078-6
Classification : 11F20, 11L05, 11M20, 11N37
Keywords: Dedekind sum; Kloosterman sum; Dirichlet character; analytic method; Gauss sum; identity 
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Huan, Le; Wang, Jingzhe; Wang, Tingting. An identity involving Dedekind sums and generalized Kloosterman sums. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 4, pp. 991-1001. doi: 10.1007/s10587-012-0078-6

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