On the mean values of Dedekind sums
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.

Mots clés : Dedekind sums, Dirichlet $L$-functions, mean value, asymptotic formula 
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     title = {On the mean values of {Dedekind} sums},
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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, Tome 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