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INVERSION OF L-FUNCTIONS, GENERAL KLOOSTERMAN SUMS WEIGHTED BY INCOMPLETE CHARACTER SUMS

Xiaobeng Zhang|Huaning Liu
대한수학회 (The Korean Mathematical Society)|2010.09|대한수학회지 (Journal of the KMS)|제47권 제5호|pp. 947-965

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참고문헌

키워드

asymptotic formulaL-functioncharacter sumgeneral Kloosterman sum
주제분류수학

초록

The main purpose of this paper is using estimates for character sums and analytic methods to study the mean value involving the incomplete character sums, 2-th power mean of the inversion of Dirichlet L-function and general Kloosterman sums, and give four interesting asymptotic formulae for it.

Abstract

The main purpose of this paper is using estimates for character sums and analytic methods to study the mean value involving the incomplete character sums, 2-th power mean of the inversion of Dirichlet L-function and general Kloosterman sums, and give four interesting asymptotic formulae for it.

참고문헌 (9)

  1. T. M. Apostol, "Introduction to Analytic Number Theory, Undergraduate Texts in Mathematics" (1976), Springer-Verlag
  2. S. Chowla, "On Kloosterman’s sum, Norkse Vid", Selbsk. Fak. Frondheim, 40, pp.70~72 (1967)
  3. T. Estermann, "On Kloosterman’s sum", Mathematica, 8, pp.83~86 (1961)
  4. H. L. Montgomery, "Mean values of character sums", Canad. J. Math., 31(3), pp.476~487 (1979)
  5. C. D. Pan, "Goldbach Conjecture" (1981), Science Press
  6. Z. Xu, "On the 2k-th power mean of the character sums over short intervals", Acta Arith., 121(2), pp.149~160 (2006)
  7. W. Zhang, "On the mean value of L-functions with the weight of character sums", J. Number Theory, 128(8), pp.2459~2466 (2008)
  8. W. Zhang, "On the general Kloosterman sums and its fourth power mean", J. Number Theory, 104(1), pp.156~161 (2004)
  9. W. Zhang, "On the 2k-th power mean of Dirichlet L-functions with the weight of general Kloosterman sums", J. Number Theory, 84(2), pp.199~213 (2000)

관련 논문AI추천

Hybrid mean value of the generalized Kloosterman sums and Dirichlet character of polynomialsWang Jingzhe대한수학회 · 대한수학회보2013 · 제50권 제2호On the general quadratic Gauss sums weighted by character sums over a short intervalTianping Zhang대한수학회 · 대한수학회보2013 · 제50권 제3호ON THE HYBRID MEAN VALUE OF GENERALIZED DEDEKIND SUMS, GENERALIZED HARDY SUMS AND KLOOSTERMAN SUMSQing Tian, Yan Wang대한수학회 · 대한수학회보2023 · 제60권 제3호A new mean value related to D. H. Lehmer's problem and Kloosterman sumsDi Han, Wenpeng Zhang대한수학회 · 대한수학회보2015 · 제52권 제1호ON THE MEAN VALUES OF L(1, χ)Wenpeng Zhang, Zhaoxia Wu대한수학회 · 대한수학회보2012 · 제49권 제6호On the r-th hyper-Kloosterman sums and a problem of D. H. LehmerXue Xifeng, Zhang Tianping대한수학회 · 대한수학회지2009 · 제46권 제4호

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