Abstract
The various properties of classical Dedekind sums S(h, q) have been investi-gated 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.
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References
T.M. Apostol: Introduction to Analytic Number Theory. Undergraduate Texts in Mathematics, Springer, New York-Heidelberg-Berlin, 1976.
T.M. Apostol: Modular Functions and Dirichlet Series in Number Theory. Graduate Texts in Mathematics, Springer, New York-Heidelberg-Berlin, 1976.
L. Carlitz: The reciprocity theorem for Dedekind sums. Pac. J. Math. 3 (1953), 523–527.
J.B. Conrey, E. Fransen, R. Klein, C. Scott: Mean values of Dedekind sums. J. Number Theory 56 (1996), 214–226.
T. Estermann: On Kloostermann’s sums. Mathematika, Lond. 8 (1961), 83–86.
K. Ireland, M. Rosen: A Classical Introduction to Modern Number Theory (Rev. and expand. version of 1972). Graduate Texts in Mathematics, Springer, New York-Heidelberg-Berlin, 1982.
Y. Liu, W. Zhang: A hybrid mean value related to the Dedekind sums and Kloosterman sums. Sci. China, Math. 53 (2010), 2543–2550; Acta Math. Sin. 27 (2011), 435–440.
W. Zhang: On the mean values of Dedekind sums. J. Théor. Nombres Bordx. 8 (1996), 429–442.
W. Zhang: A sum analogous to Dedekind sums and its hybrid mean value formula. Acta Arith. 107 (2003), 1–8.
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The research has been supported by the N. S. F. (11071194) of P.R.China.
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Huan, L., Wang, J. & Wang, T. An identity involving Dedekind sums and generalized Kloosterman sums. Czech Math J 62, 991–1001 (2012). https://doi.org/10.1007/s10587-012-0078-6
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DOI: https://doi.org/10.1007/s10587-012-0078-6