On the mean values of Dedekind sums
Journal de théorie des nombres de Bordeaux, Volume 8 (1996) no. 2, pp. 429-442.

In this paper we study the asymptotic behavior of the mean value of Dedekind sums, and give a sharper asymptotic formula.

On étudie dans ce papier le comportement asymptotique de valeurs moyennes de sommes de Dedekind. On donne en particulier une formule asymptotique améliorant un résultat antérieur.

Keywords: Dedekind sums, Dirichlet $L$-functions, mean value, asymptotic formula 
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     title = {On the mean values of {Dedekind} sums},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {429--442},
     publisher = {Universit\'e Bordeaux I},
     volume = {8},
     number = {2},
     year = {1996},
     zbl = {0871.11033},
     mrnumber = {1438480},
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     url = {https://jtnb.centre-mersenne.org/item/JTNB_1996__8_2_429_0/}
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Wenpeng Zhang. On the mean values of Dedekind sums. Journal de théorie des nombres de Bordeaux, Volume 8 (1996) no. 2, pp. 429-442. https://jtnb.centre-mersenne.org/item/JTNB_1996__8_2_429_0/

1 Tom M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976. | MR | Zbl

2 _____, Modular Functions and Dirichlet Series in Number Theory, Springer-Verlag, New York, 1976. | MR

3 L. Carlitz, The reciprocity theorem for Dedekind sums, Pacific J. Math. 3 (1953), 523-527. | MR | Zbl

4 J.B. Conrey, Eric Fransen, Robert Klein and Clayton Scott, Mean values of Dedekind sums, J. Number Theory 56 (1996), 214-226. | MR | Zbl

5 L.J. Mordell, The reciprocity formula for Dedekind sums, Amer. J. Math. 73 (1951), 593-598. | MR | Zbl

6 H. Rademacher, On the transformation of log η(τ), J. Indian Math. Soc. 19 (1955), 25-30. | Zbl

7 H. Rademacher and E. Grosswald, Dedekind Sums, The Carus Mathematical Monographs, Math. Assoc. Amer., Washington D.C., 1972. | MR | Zbl

8 H. Walum, An exact formula for an average of L-series, Illinois J. Math. 26 (1982), 1-3. | MR | Zbl

9 Zhang Wenpeng, Lecture Notes in Contemporary Mathematics, Science Press, Beijing, China, 1989, pp. 173-179. | MR

10 Zhang Wenpeng, A note on a class mean square values of L-functions, Journal of Northwest University 20 (1990), 9-12. | MR | Zbl

11 D.E. Knuth, Notes on generalized Dedekind sums, Acta Arith. 33 (1977), 297-325. | MR | Zbl