On the mean values of Dedekind sums
Wenpeng Zhang
Journal de Théorie des Nombres de Bordeaux, Tome 8 (1996) no. 2, pp. 429-442.

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.

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

DOI : https://doi.org/10.5802/jtnb.179
Mots clés : Dedekind sums, Dirichlet L-functions, mean value, asymptotic formula 
@article{JTNB_1996__8_2_429_0,
     author = {Zhang, Wenpeng},
     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},
     doi = {10.5802/jtnb.179},
     zbl = {0871.11033},
     mrnumber = {1438480},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.179/}
}
Wenpeng Zhang. On the mean values of Dedekind sums. Journal de Théorie des Nombres de Bordeaux, Tome 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