On hybrid mean value of Dedekind sums and two-term exponential sums

Tingting Wang, Wenpeng Zhang

Front. Math. China ›› 2011, Vol. 6 ›› Issue (3) : 557-563.

PDF(104 KB)
PDF(104 KB)
Front. Math. China ›› 2011, Vol. 6 ›› Issue (3) : 557-563. DOI: 10.1007/s11464-011-0132-y
Research Article
RESEARCH ARTICLE

On hybrid mean value of Dedekind sums and two-term exponential sums

Author information +
History +

Abstract

In this paper, we use the elementary and analytic methods to study the computational problem of one kind mean value involving the classical Dedekind sums and two-term exponential sums, and give two exact computational formulae for them.

Keywords

Dedekind sums / two-term exponential sums / mean value / computational formula

Cite this article

Download citation ▾
Tingting Wang, Wenpeng Zhang. On hybrid mean value of Dedekind sums and two-term exponential sums. Front. Math. China, 2011, 6(3): 557‒563 https://doi.org/10.1007/s11464-011-0132-y

References

[1.]
Apostol T. M. Modular Functions and Dirichlet Series in Number Theory, 1976, New York: Springer-Verlag.
[2.]
Cochrane T. Exponential sums modulo prime powers. Acta Arithmetica, 2002, 101, 131-149
CrossRef Google scholar
[3.]
Cochrane T., Pinner C. A further refinement of Mordell’s bound on exponential sums. Acta Arithmetica, 2005, 116, 35-41
CrossRef Google scholar
[4.]
Cochrane T., Pinner C. Using Stepanov’s method for exponential sums involving rational functions. Journal of Number Theory, 2006, 116, 270-292
CrossRef Google scholar
[5.]
Cochrane T., Zheng Z. Upper bounds on a two-term exponential sums. Sci China, Ser A, 2001, 44, 1003-1015
CrossRef Google scholar
[6.]
Conrey J. B., Fransen E., Klein R., Scott C. Mean values of Dedekind sums. Journal of Number Theory, 1996, 56, 214-226
CrossRef Google scholar
[7.]
Hua L. K. Introduction to Number Theory, 1979, Beijing: Science Press.
[8.]
Jia Chaohua. On the mean value of Dedekind sums. Journal of Number Theory, 2001, 87, 173-188
CrossRef Google scholar
[9.]
Rademacher H. On the transformation of log η(τ). J Indian Math Soc, 1955, 19, 25-30
[10.]
Rademacher H. Dedekind Sums. Carus Mathematical Monographs, 1972, Washington DC: Math Assoc Amer.
[11.]
Zhang W. On the mean values of Dedekind Sums. Journal de Théorie des Nombres de Bordeaux, 1996, 8, 429-442
[12.]
Zhang W. A note on the mean square value of the Dedekind sums. Acta Mathematica Hungarica, 2000, 86, 275-289
CrossRef Google scholar
AI Summary AI Mindmap
PDF(104 KB)

Accesses

Citations

Detail

Sections
Recommended

/