Abstract
The main purpose of this paper is, using the mean-value theorem of Dirichlet l-functions, to study the distribution properties of the hybrid mean value involving certain Hardy sums and Ramanujan sum, and give four interesting identities.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Rademacher, H.: “Dedekind Sums” Carus Mathematical Monographs, Math. Assoc. Amer., Washington D. C., 1972
Berndt, B. C.: Analytic Eisenstein series, theta–functions, and series relations in the spirit of Ramanujan. J. Reine Angew. Math., 303/304, 332–365 (1978)
Sitaramachandraro, R.: Dedekind and Hardy sums. Acta Arithmetica, 48, 325–340 (1987)
Zhang, W. P., Yi, Y.: On the 2m–th power mean of certain Hardy sums. Soochow Journal of Mathematics, 26, 73–84 (2000)
Zhang, W. P., Yi, Y.: On a sum analogous to the Dedekind sum and its first power mean value formula. Journal of Mathematical Analysis and Applications, 256, 542–555 (2001)
Zhang, W. P.: On the mean values of Dedekind Sums. Journal de Theorie des Nombres, 8, 429–442 (1996)
Pan, C. D., Pan, C. B.: Goldbach Conjecture, Science Press, Beijing, 24, 1981
Author information
Authors and Affiliations
Corresponding author
Additional information
This work is supported by the NSF (10271093) and the PNSF of P. R. China
Rights and permissions
About this article
Cite this article
Liu, H.Y., Zhang, W.P. Some Identities Involving Certain Hardy Sums and Ramanujan Sum. Acta Math Sinica 21, 109–116 (2005). https://doi.org/10.1007/s10114-004-0345-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10114-004-0345-z