Geodesic
On the mean value of Dedekind sum weighted by the quadratic Gauss sum
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 357-367
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Various properties of classical Dedekind sums $S(h, q)$ have been investigated by many authors. For example, Wenpeng Zhang, On the mean values of Dedekind sums, J. Théor. Nombres Bordx, 8 (1996), 429–442, studied the asymptotic behavior of the mean value of Dedekind sums, and H. Rademacher and E. Grosswald, Dedekind Sums, The Carus Mathematical Monographs No. 16, The Mathematical Association of America, Washington, D.C., 1972, studied the related properties. In this paper, we use the algebraic method to study the computational problem of one kind of mean value involving the classical Dedekind sum and the quadratic Gauss sum, and give several exact computational formulae for it.
Various properties of classical Dedekind sums $S(h, q)$ have been investigated by many authors. For example, Wenpeng Zhang, On the mean values of Dedekind sums, J. Théor. Nombres Bordx, 8 (1996), 429–442, studied the asymptotic behavior of the mean value of Dedekind sums, and H. Rademacher and E. Grosswald, Dedekind Sums, The Carus Mathematical Monographs No. 16, The Mathematical Association of America, Washington, D.C., 1972, studied the related properties. In this paper, we use the algebraic method to study the computational problem of one kind of mean value involving the classical Dedekind sum and the quadratic Gauss sum, and give several exact computational formulae for it.
DOI : 10.1007/s10587-013-0021-5
Classification : 11F20, 11L40
Keywords: Dedekind sum; quadratic Gauss sum; mean value; identity 
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Wang, Tingting; Zhang, Wenpeng. On the mean value of Dedekind sum weighted by the quadratic Gauss sum. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 357-367. doi: 10.1007/s10587-013-0021-5

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