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关于Dedekind和的均值公式

  • 任正民 ,
  • 雷德利
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  • 1. 北京石油化工学院数理部, 北京 102600;
    2. 西北大学数学系, 西安 710069
任正民, 男, 1964 年7 月生, 讲师

收稿日期: 2002-01-09

  修回日期: 2002-03-25

  网络出版日期: 2002-07-18

On the Mean Value Formula of Dedekind Sums

  • REN Zheng Min ,
  • LEI De Li
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  • 1. Beijing Institute of Petro Chemical Technology, Beijing 102600;
    2. Department of Mathematics, Northwest University, Xi’an 710069

Received date: 2002-01-09

  Revised date: 2002-03-25

  Online published: 2002-07-18

摘要

利用Dedekind和的值分布性质,研究Dedekind和的渐近性质,在J.B.Conrey研究的基础上,完善了形如 |S(h,k)|n 的Dedekind和的均值问题的研究

本文引用格式

任正民 , 雷德利 . 关于Dedekind和的均值公式[J]. 中国科学院大学学报, 2002 , 19(4) : 376 -381 . DOI: 10.7523/j.issn.2095-6134.2002.4.007

Abstract

The main purpose is using the property of distribution of values of Dedekind sums to study the asymptotic propert ies of Dedekind sums. On the basis of J. B. Conreycs research, perfect the study of mean value problem of Dedekind sums in the form of 6|S( h,k)|n.

参考文献

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[2] Carlit z L. The reciprocity Theorem of Dedekin d Sums. Pacific J of Math, 1953, 3: 513~ 522

[3] L J Mordell. The reciprocity f ormula for Dedekind sums. Amer J Math, 1951, 73: 593~ 598

[4] H Rademacher. On the transformation of log G(S). J Indian Math S oc, 1955, 19: 25~ 30

[5] H Rademacher. " Dedek ind Sums" Carus Mathematical Monographs. Math Assoc Am er, 1972

[6] Conrey J B, Eric Fransen, Robert Klein, Clayton Scott. Mean values of Dedekind sums. Journal of Number Theory, 1996, 56: 214~ 226

[7] Walum H. An exact formula for an average of L-series. Illinois J Math, 1982, 26: 1~ 3

[8] Wenpeng Zhang. On the mean values of Dedekind Sums. Journal de Theorie des Nombres, 1996, 8: 429~ 442

[9] Xiali He, Wenpeng Zhang. On the mean value formula of Dedekind sums. Acta Mathematica Sinica, English Series, 1999

[10] Hardy G H, Wright E M. Anintroduction to the theory of Numbers. 5th ed1 London:Oxford University Press, 1981

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