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有理函数上的狄雷克莱特征

  • 刘春雷 ,
  • 徐兰菊
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  • 1. 北京师范大学 北京100875;
    2. 清华大学 北京100084

网络出版日期: 2005-01-15

Dirichlet Character Sums of Rational Functions

  • Liu Chunlei ,
  • Xu Lanju
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  • 1. Beijing Normal University, Beijing 100875, China;
    2. Tsinghua University, Beijing 100084, China.

Online published: 2005-01-15

Supported by

supported by NSFC (10371132)

摘要

对有理函数的特征和得到了一个估计,这个估计是华罗庚关于三角和的一个估计的类比。

本文引用格式

刘春雷 , 徐兰菊 . 有理函数上的狄雷克莱特征[J]. 中国科学院大学学报, 2005 , 22(1) : 1 -10 . DOI: 10.7523/j.issn.2095-6134.2005.1.001

Abstract

Hua's estimate is obtained for some Dirichlet character sums of rational functions.

参考文献

[1] Hua LK.On exponential sums .J .Chinese Math .Soc ., 1940 , 2 :301—312

[2] Ismoilov D.Complete charact er sums of polynomials .Trudy Math .Inst Steklov ,1991 , 200 :171—184

[3] Liu CL.Dirichlet character sums .Acta Arith ., LXXXVIII .1999 , 4:299—309

[4] Liu CL.Character sums of rational functions .Science in China , Ser .A ,1995 , 28(6):561—578

[5] Liu CL.Character sums of rational functions over local f ields.Acta Arith ., LXXV .1996 , 3 :195—204

[6] Cochrane T, Liu CL, Zheng ZY .Upper bounds on character sums with rat ional function entries .Acta Math .Sinica(in press)

[7] Weil A .On some exponential sums .Proc .Nat .Acad .Sci .USA , 1948 , 34 :204—207

[8] Ding P , Qi MG.Further estimate of complete trigonometric sums .J .Tsinghua Univ ., 1989 , 29(6):74—85

[9] Chen JR.On professor Hua' s estimate of exponential sums.Sci .S inica , 1977 , 20(6):171—179

[10] Lu MG .Estimate of a complete trigonometric sum .Scientia Sinica , Ser .A ,1985 , 28(6):561—578

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