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A Mean Value of Cochrane Sum 被引量：4

A Mean Value of Cochrane Sum
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摘要 Let q 〉 4 be an integer. The main purpose of this paper is to study the mean value of Cochrane sum C（a, q） in quarter intervals, and obtain a sharp asymptotic formula for it. Let q 〉 4 be an integer. The main purpose of this paper is to study the mean value of Cochrane sum C（a, q） in quarter intervals, and obtain a sharp asymptotic formula for it.
作者 Zhe Feng XU
机构地区 College of Science Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2009年第2期223-234,共12页 数学学报（英文版）
基金 supported by China Postdoctoral Science Foundation funded project (20080430202) the N.S.F.(10671155) of P.R.China
关键词 Dedekind sum Cochrane sums mean value asymptotic formula Dedekind sum, Cochrane sums, mean value, asymptotic formula
分类号 O174 [理学—基础数学]
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参考文献11

  • 1Carlitz, L.: The reciprocity theorem of Dedekind sums. Pacific J. Math., 3, 513-522 (1953)
  • 2Rademacher, H.: On the transformation oflog η(T). J. Indian. Math. Soc., 19, 25-30(1955)
  • 3Conrey, J. B., Fransen, E., Klein, R., Scott, C.: Mean values of Dedekind sums. J. Number Theory, 41, 27-31 (1982)
  • 4Zhang, W. P.: A note on the mean square valueof the Dedekind sums. Acta Math. Hungar., 86, 275-289 (2000)
  • 5Zhang, W. P.: On a sum analogous to Dedekind sum and its mean square value formula. International J. of Math. and Math. Sci., 32, 47-55 (2002)
  • 6Zhang, W. P.: On a Cochrane sum and its hybrid mean value formula. J. Math. Anal. Appl., 267, 89-96 (2002)
  • 7Zhang, W. P., Liu, H. N.: A note on the Cochrane sum and its hybrid mean value formula. J. Math. Anal. Appl., 288, 646-659 (2003)
  • 8Xu, Z. F., Zhang, W. P.: On the order of the high-dimensional Cochrane sum and its mean value. J. Number Theory, 117, 131-145 (2006)
  • 9Takeo, F.: On Kronecker's limit formula for Dirichlet series with periodic coefficients. Acta Arith., 55, 59-73 (1990)
  • 10Zhang,W. P.: On the mean values of Dedekind Sums. Journal de Theorie des Nombres, 8, 429-442 (1996)

同被引文献18

  • 1任刚练,张文鹏.两个新数论函数的渐近性质[J].陕西师范大学学报（自然科学版）,2007,35(1):17-20. 被引量：1
  • 2Liu Hongyan,Zhang Wenpeng. On a Generalized Cochrane Sum and Its Hybrid Mean Value Formula [J]. The Ramanu-jan Journah2005(9) :373-380.
  • 3Tom M Apostoi. Modular Functions and Dirichlet Series in Number Theory [M]. New York:Springer-Verlag. 1976.
  • 4Xu Zhefeng,Zhang Wenpeng. On the order of the high-dimensional Cochrane sum and its mean value [J]. Journal ofNumber Theory ,2006 ,117 : 131-145.
  • 5Tom M Apostoi. Introduction to Analytic Number Theory [M]. New York:Springer-Verlag, 1976.
  • 6徐哲峰,张文鹏,Dirichlet特征及其应用[M].北京:科学出版社,2008.
  • 7Wenpeng Zhang. On a Cochrane sum and its hybrid mean value formula [J], Journal of Mathematical Analysis and itsApplications, 2002 ,267 : 89-96.
  • 8Juan C Peral. Character sums and explicit estimates for functions [J]. Contemporary Mathematics, 1995.189 :449-459.
  • 9Zhang Wenpeng. On a sum analogous to Dedekind sum and its mean square value formula[J]. International Journal of Mathematics and Mathematical Sciences, 2002,32(1):47-55.
  • 10Liu Hongyan, Zhang Wenpeng. On a generalized cochrane sum and its hybrid mean value formula[J]. The Ramanujan Journal, 2005,9(3):373-380.

引证文献4

二级引证文献3

Acta Mathematica Sinica,English Series
2009年 第2期

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