On the mean values of Dedekind sums

Wenpeng Zhang

Journal de théorie des nombres de Bordeaux (1996)

  • Volume: 8, Issue: 2, page 429-442
  • ISSN: 1246-7405

Abstract

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In this paper we study the asymptotic behavior of the mean value of Dedekind sums, and give a sharper asymptotic formula.

How to cite

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Zhang, Wenpeng. "On the mean values of Dedekind sums." Journal de théorie des nombres de Bordeaux 8.2 (1996): 429-442. <http://eudml.org/doc/247823>.

@article{Zhang1996,
abstract = {In this paper we study the asymptotic behavior of the mean value of Dedekind sums, and give a sharper asymptotic formula.},
author = {Zhang, Wenpeng},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {Dedekind sums; Dirichlet $L$-functions; mean value; asymptotic formula; mean values of Dedekind sums},
language = {eng},
number = {2},
pages = {429-442},
publisher = {Université Bordeaux I},
title = {On the mean values of Dedekind sums},
url = {http://eudml.org/doc/247823},
volume = {8},
year = {1996},
}

TY - JOUR
AU - Zhang, Wenpeng
TI - On the mean values of Dedekind sums
JO - Journal de théorie des nombres de Bordeaux
PY - 1996
PB - Université Bordeaux I
VL - 8
IS - 2
SP - 429
EP - 442
AB - In this paper we study the asymptotic behavior of the mean value of Dedekind sums, and give a sharper asymptotic formula.
LA - eng
KW - Dedekind sums; Dirichlet $L$-functions; mean value; asymptotic formula; mean values of Dedekind sums
UR - http://eudml.org/doc/247823
ER -

References

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  1. 1 Tom M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976. Zbl0335.10001MR434929
  2. 2 _____, Modular Functions and Dirichlet Series in Number Theory, Springer-Verlag, New York, 1976. MR422157
  3. 3 L. Carlitz, The reciprocity theorem for Dedekind sums, Pacific J. Math.3 (1953), 523-527. Zbl0057.03703MR56020
  4. 4 J.B. Conrey, Eric Fransen, Robert Klein and Clayton Scott, Mean values of Dedekind sums, J. Number Theory56 (1996), 214-226. Zbl0851.11028MR1373548
  5. 5 L.J. Mordell, The reciprocity formula for Dedekind sums, Amer. J. Math.73 (1951), 593-598. Zbl0042.27401MR42449
  6. 6 H. Rademacher, On the transformation of log η(τ), J. Indian Math. Soc.19 (1955), 25-30. Zbl0064.32703
  7. 7 H. Rademacher and E. Grosswald, Dedekind Sums, The Carus Mathematical Monographs, Math. Assoc. Amer., Washington D.C., 1972. Zbl0251.10020MR357299
  8. 8 H. Walum, An exact formula for an average of L-series, Illinois J. Math.26 (1982), 1-3. Zbl0464.10030MR638548
  9. 9 Zhang Wenpeng, Lecture Notes in Contemporary Mathematics, Science Press, Beijing, China, 1989, pp. 173-179. MR1180537
  10. 10 Zhang Wenpeng, A note on a class mean square values of L-functions, Journal of Northwest University20 (1990), 9-12. Zbl0728.11041MR1077163
  11. 11 D.E. Knuth, Notes on generalized Dedekind sums, Acta Arith.33 (1977), 297-325. Zbl0326.10007MR485660

Citations in EuDML Documents

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  1. Wenpeng Zhang, On the hybrid mean value of Dedekind sums and Hurwitz zeta-function
  2. Jianghua Li, Wenpeng Zhang, A hybrid mean value related to Dedekind sums
  3. Tingting Wang, Wenpeng Zhang, On the mean value of Dedekind sum weighted by the quadratic Gauss sum
  4. Jing Guo, Xiaoxue Li, On the k -polygonal numbers and the mean value of Dedekind sums
  5. Chang Leran, Li Xiaoxue, The hybrid mean value of Dedekind sums and two-term exponential sums
  6. Hai Yang, A hybrid mean value of the Dedekind sums
  7. Xiaowei Pan, Wenpeng Zhang, On Lehmer's problem and Dedekind sums
  8. Le Huan, Jingzhe Wang, Tingting Wang, An identity involving Dedekind sums and generalized Kloosterman sums
  9. Xiaoyan Guo, Wenpeng Zhang, A hybrid mean value related to certain Hardy sums and Kloosterman sums

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