Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON THE FOURTH POWER MEAN OF GENERALIZED TWO-TERM EXPONENTIAL SUMS

  • Received : 2011.07.22
  • Published : 2013.01.31
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Abstract

In this paper, we use the elementary method and the theory of complex functions to study the computational problem of the fourth power mean of the generalized two-term exponential sums, and give two exact identities for them.

Keywords

References

  1. Tom M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976.
  2. T. Cochrane and C. Pinner, A further refinement of Mordell's bound on exponential sums, Acta Arith. 116 (2005), no. 1, 35-41. https://doi.org/10.4064/aa116-1-4
  3. T. Cochrane and C. Pinner, Using Stepanov's method for exponential sums involving rational functions, J. Number Theory 116 (2006), no. 2, 270-292. https://doi.org/10.1016/j.jnt.2005.04.001
  4. T. Cochrane and Z. Y. Zheng, Pure and mixed exponential sums, Acta Arith. 91 (1999), no. 3, 249-278. https://doi.org/10.4064/aa-91-3-249-278
  5. T. Cochrane and Z. Y. Zheng, Upper bounds on a two-term exponential sums, Sci. China Ser. A 44 (2001), no. 8, 1003-1015. https://doi.org/10.1007/BF02878976
  6. L. K. Hua, Introduction to Number Theory, Science Press, Beijing, 1979.
  7. V. Pigno and C. Pinner, Twisted monomial Gauss sums modulo prime powers, http://www.math.ksu.edu/ pinner/Pubs/tgauss4a.pdf.
  8. A. Weil, On some exponential sums, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 204-207. https://doi.org/10.1073/pnas.34.5.204
  9. W. Zhang, Moments of generalized quadratic Gauss sums weighted by L-functions, J. Number Theory 92 (2002), no. 2, 304-314. https://doi.org/10.1006/jnth.2001.2715

Cited by

  1. On the Fourth Power Mean of the Two-Term Exponential Sums vol.2014, 2014, https://doi.org/10.1155/2014/724840
  2. The fourth power mean of the generalized two-term exponential sums and its upper and lower bound estimates vol.2013, pp.1, 2013, https://doi.org/10.1186/1029-242X-2013-504