Weixia Liu
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 19, 2013, Number 2, Pages 60—68
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Weixia Liu
Straits Institute, Minjiang University
Fuzhou, P. R. China
Abstract
The main purpose of this paper is using the mean values of Dirichlet L-functions and estimates for character sums to study the mean values of Dedekind sums over short intervals.
Keywords
- Dedekind sums
- Mean value
- Short interval
- Dirichlet L-function
AMS Classification
- 11M06
- 11M32
References
- Walum, H. An exact formula for an average of L-series, Illinois J. Math., 26 (1982), 1–3.
- Conrey, J. B., E. Fransen, R. Klein, C. Scott. Mean values of Dedekind sums, J. Number Theory, Vol. 56, 1996, 214–226.
- Jia, C. On the Mean Values of Dedekind sums, J. Number Theory, Vol. 87, 2001, 173–188.
- Zhang, W., X. Wang. On the fourth power mean of the character sums over short intervals, Acta Math. Sinica, Vol. 23, 2007, 153–164.
- Zhang, W. On the mean values of Dedekind sums, J. Théor. Nombres Bordeaux. Vol. 8, 1996, 429–442.
- Xu, Z., W. Zhang. The mean value of Hardy sums over short intervals, Proc. Royal Soc. Edinburgh, Vol. 137A, 2007, 885–894.
- Takeo, F. On Kronecker’s limit formula for Dirichlet series with periodic coefficients, Acta Arith., Vol. 55, 1990, 59–73.
- Apostol, T. M. Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976.
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Cite this paper
APALiu, W. (2013). Note on some explicit formulae for twin prime counting function. Notes on Number Theory and Discrete Mathematics, 19(2), 60-68.
ChicagoLiu, Weixia. “Note on Some Explicit Formulae for Twin Prime Counting Function.” Notes on Number Theory and Discrete Mathematics 19, no. 2 (2013): 60-68.
MLALiu, Weixia. “Note on Some Explicit Formulae for Twin Prime Counting Function.” Notes on Number Theory and Discrete Mathematics 19.2 (2013): 60-68. Print.