On the mean values of Dedekind sums
Journal de théorie des nombres de Bordeaux (1996)
- Volume: 8, Issue: 2, page 429-442
- ISSN: 1246-7405
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topZhang, 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
top- 1 Tom M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976. Zbl0335.10001MR434929
- 2 _____, Modular Functions and Dirichlet Series in Number Theory, Springer-Verlag, New York, 1976. MR422157
- 3 L. Carlitz, The reciprocity theorem for Dedekind sums, Pacific J. Math.3 (1953), 523-527. Zbl0057.03703MR56020
- 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 L.J. Mordell, The reciprocity formula for Dedekind sums, Amer. J. Math.73 (1951), 593-598. Zbl0042.27401MR42449
- 6 H. Rademacher, On the transformation of log η(τ), J. Indian Math. Soc.19 (1955), 25-30. Zbl0064.32703
- 7 H. Rademacher and E. Grosswald, Dedekind Sums, The Carus Mathematical Monographs, Math. Assoc. Amer., Washington D.C., 1972. Zbl0251.10020MR357299
- 8 H. Walum, An exact formula for an average of L-series, Illinois J. Math.26 (1982), 1-3. Zbl0464.10030MR638548
- 9 Zhang Wenpeng, Lecture Notes in Contemporary Mathematics, Science Press, Beijing, China, 1989, pp. 173-179. MR1180537
- 10 Zhang Wenpeng, A note on a class mean square values of L-functions, Journal of Northwest University20 (1990), 9-12. Zbl0728.11041MR1077163
- 11 D.E. Knuth, Notes on generalized Dedekind sums, Acta Arith.33 (1977), 297-325. Zbl0326.10007MR485660
Citations in EuDML Documents
top- Wenpeng Zhang, On the hybrid mean value of Dedekind sums and Hurwitz zeta-function
- Jianghua Li, Wenpeng Zhang, A hybrid mean value related to Dedekind sums
- Tingting Wang, Wenpeng Zhang, On the mean value of Dedekind sum weighted by the quadratic Gauss sum
- Jing Guo, Xiaoxue Li, On the -polygonal numbers and the mean value of Dedekind sums
- Xiaowei Pan, Wenpeng Zhang, On Lehmer's problem and Dedekind sums
- Hai Yang, A hybrid mean value of the Dedekind sums
- Le Huan, Jingzhe Wang, Tingting Wang, An identity involving Dedekind sums and generalized Kloosterman sums
- Xiaoyan Guo, Wenpeng Zhang, A hybrid mean value related to certain Hardy sums and Kloosterman sums
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