Abstract
The main purpose of this paper is using the properties of character sum and the analytic method to study a hybrid mean value problem related to the Dedekind sums and Kloosterman sums, and give some interesting mean value formulae and identities for it.
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References
Apostol T M. Introduction to Analytic Number Theory. New York: Springer-Verlag, 1976
Apostol T M. Modular Functions and Dirichlet Series in Number Theory. New York: Springer-Verlag, 1976
Carlitz L. The reciprocity theorem of Dedekind sums. Pacific J Math, 1953, 3:513–522.
Conrey J B, Fransen E, Klein R, et al. Mean values of Dedekind sums. J Number Theory, 1996, 56:214–226
Jia C H. On the mean value of Dedekind sums. J Number Theory, 2001, 87:173–188
Rademacher H, Grosswald E. Dedekind Sums. In: Carus Mathematical Monographs, vol. 16. Washington DC: Mathematical Association of America, 1972
Zhang W P. On the mean values of Dedekind sums. J Théor Nombres Bordeaux, 1996, 8:429–442
Zhang W P. A note on the mean square value of the Dedekind sums. Acta Math Hungar, 2000, 86:275–289
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Dedicated to Professor Wang Yuan on the Occasion of his 80th Birthday
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Zhang, W., Liu, Y. A hybrid mean value related to the Dedekind sums and Kloosterman sums. Sci. China Math. 53, 2543–2550 (2010). https://doi.org/10.1007/s11425-010-3153-1
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DOI: https://doi.org/10.1007/s11425-010-3153-1