Weixia Liu

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 19, 2013, Number 2, Pages 60—68

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## Details

### Authors and affiliations

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.

## Related papers

## 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.