On the mean values of Dedekind sums over short intervals

Weixia Liu
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 19, 2013, Number 2, Pages 60—68
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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

  1. Walum, H. An exact formula for an average of L-series, Illinois J. Math., 26 (1982), 1–3.
  2. Conrey, J. B., E. Fransen, R. Klein, C. Scott. Mean values of Dedekind sums, J. Number Theory, Vol. 56, 1996, 214–226.
  3. Jia, C. On the Mean Values of Dedekind sums, J. Number Theory, Vol. 87, 2001, 173–188.
  4. Zhang, W., X. Wang. On the fourth power mean of the character sums over short intervals, Acta Math. Sinica, Vol. 23, 2007, 153–164.
  5. Zhang, W. On the mean values of Dedekind sums, J. Théor. Nombres Bordeaux. Vol. 8, 1996, 429–442.
  6. Xu, Z., W. Zhang. The mean value of Hardy sums over short intervals, Proc. Royal Soc. Edinburgh, Vol. 137A, 2007, 885–894.
  7. Takeo, F. On Kronecker’s limit formula for Dirichlet series with periodic coefficients, Acta Arith., Vol. 55, 1990, 59–73.
  8. Apostol, T. M. Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976.

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Cite this paper

APA

Liu, W. (2013). Note on some explicit formulae for twin prime counting function. Notes on Number Theory and Discrete Mathematics, 19(2), 60-68.

Chicago

Liu, Weixia. “Note on Some Explicit Formulae for Twin Prime Counting Function.” Notes on Number Theory and Discrete Mathematics 19, no. 2 (2013): 60-68.

MLA

Liu, Weixia. “Note on Some Explicit Formulae for Twin Prime Counting Function.” Notes on Number Theory and Discrete Mathematics 19.2 (2013): 60-68. Print.

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