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.

DOI: 10.5802/jtnb.179
Keywords: Dedekind sums, Dirichlet L-functions, mean value, asymptotic formula
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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. doi : 10.5802/jtnb.179. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.179/

1 Tom M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976. | MR: 434929 | Zbl: 0335.10001

2 _____, Modular Functions and Dirichlet Series in Number Theory, Springer-Verlag, New York, 1976. | MR: 422157

3 L. Carlitz, The reciprocity theorem for Dedekind sums, Pacific J. Math. 3 (1953), 523-527. | MR: 56020 | Zbl: 0057.03703

4 J.B. Conrey, Eric Fransen, Robert Klein and Clayton Scott, Mean values of Dedekind sums, J. Number Theory 56 (1996), 214-226. | MR: 1373548 | Zbl: 0851.11028

5 L.J. Mordell, The reciprocity formula for Dedekind sums, Amer. J. Math. 73 (1951), 593-598. | MR: 42449 | Zbl: 0042.27401

6 H. Rademacher, On the transformation of log η(τ), J. Indian Math. Soc. 19 (1955), 25-30. | Zbl: 0064.32703

7 H. Rademacher and E. Grosswald, Dedekind Sums, The Carus Mathematical Monographs, Math. Assoc. Amer., Washington D.C., 1972. | MR: 357299 | Zbl: 0251.10020

8 H. Walum, An exact formula for an average of L-series, Illinois J. Math. 26 (1982), 1-3. | MR: 638548 | Zbl: 0464.10030

9 Zhang Wenpeng, Lecture Notes in Contemporary Mathematics, Science Press, Beijing, China, 1989, pp. 173-179. | MR: 1180537

10 Zhang Wenpeng, A note on a class mean square values of L-functions, Journal of Northwest University 20 (1990), 9-12. | MR: 1077163 | Zbl: 0728.11041

11 D.E. Knuth, Notes on generalized Dedekind sums, Acta Arith. 33 (1977), 297-325. | MR: 485660 | Zbl: 0326.10007

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