Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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INVERSION OF L-FUNCTIONS, GENERAL KLOOSTERMAN SUMS WEIGHTED BY INCOMPLETE CHARACTER SUMS

  • Zhang, Xiaobeng (DEPARTMENT OF MATHEMATICS NORTHWEST UNIVERSITY, DEPARTMENT OF APPLIED MATHEMATICS AND PHYSICS XI'AN UNIVERSITY OF POST AND TELECOMMUNICATIONS) ;
  • Liu, Huaning (DEPARTMENT OF MATHEMATICS NORTHWEST UNIVERSITY)
  • Received : 2008.12.12
  • Published : 2010.09.01
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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.

Keywords

References

  1. T. M. Apostol, Introduction to Analytic Number Theory, Undergraduate Texts in Mathematics. Springer-Verlag, New York-Heidelberg, 1976.
  2. S. Chowla, On Kloosterman’s sum, Norkse Vid. Selbsk. Fak. Frondheim 40 (1967), 70-72.
  3. T. Estermann, On Kloosterman’s sum, Mathematica 8 (1961), 83-86.
  4. H. L. Montgomery and R. C. Vaughan, Mean values of character sums, Canad. J. Math. 31 (1979), no. 3, 476-487. https://doi.org/10.4153/CJM-1979-053-2
  5. C. D. Pan and C. B. Pan, Goldbach Conjecture, Science Press, Beijing, 1981.
  6. Z. Xu and W. Zhang, On the 2k-th power mean of the character sums over short intervals, Acta Arith. 121 (2006), no. 2, 149-160. https://doi.org/10.4064/aa121-2-4
  7. W. Zhang, On the mean value of L-functions with the weight of character sums, J. Number Theory 128 (2008), no. 8, 2459-2466. https://doi.org/10.1016/j.jnt.2007.11.008
  8. W. Zhang, On the general Kloosterman sums and its fourth power mean, J. Number Theory 104 (2004), no. 1, 156-161. https://doi.org/10.1016/S0022-314X(03)00154-9
  9. W. Zhang, Y. Yi, and X. He, On the 2k-th power mean of Dirichlet L-functions with the weight of general Kloosterman sums, J. Number Theory 84 (2000), no. 2, 199-213. https://doi.org/10.1006/jnth.2000.2515