Abstract and Applied Analysis

On the Sixth Power Mean Value of the Generalized Three-Term Exponential Sums

Yahui Yu and Wenpeng Zhang

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Abstract

The main purpose of this paper is using the estimate for trigonometric sums and the properties of the congruence equations to study the computational problem of one kind sixth power mean value of the generalized three-term exponential sums and give an exact computational formula for it.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 474726, 4 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412273315

Digital Object Identifier
doi:10.1155/2014/474726

Mathematical Reviews number (MathSciNet)
MR3198197

Zentralblatt MATH identifier
07022447

Citation

Yu, Yahui; Zhang, Wenpeng. On the Sixth Power Mean Value of the Generalized Three-Term Exponential Sums. Abstr. Appl. Anal. 2014 (2014), Article ID 474726, 4 pages. doi:10.1155/2014/474726. https://projecteuclid.org/euclid.aaa/1412273315


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References

  • T. M. Apostol, “An extension of the Lehmers' picturesque exponential sums,” Mathematics of Computation, vol. 61, no. 203, pp. 25–28, 1993.
  • B. C. Berndt, “On Gaussian sums and other exponential sums with periodic coefficients,” Duke Mathematical Journal, vol. 40, pp. 145–156, 1973.
  • T. Cochrane and C. Pinner, “Using Stepanov's method for exponential sums involving rational functions,” Journal of Number Theory, vol. 116, no. 2, pp. 270–292, 2006.
  • T. Cochrane and Z. Zheng, “Upper bounds on a two-term exponential sum,” Science in China A: Mathematics, vol. 44, no. 8, pp. 1003–1015, 2001.
  • X. Du and D. Han, “On the fourth power mean of the three term exponential sums,” Journal of Northwest University, vol. 43, pp. 541–544, 2013.
  • L. K. Hua, Additive Prime Number Theory, Science Press, Beijing, China, 1957.
  • W. M. Schmidt, Equations over Finite Fields: An Elementary Approach, vol. 536 of Lecture Notes in Mathematics, Springer, New York, NY, USA, 1976.
  • A. Weil, “On some exponential sums,” Proceedings of the National Academy of Sciences of the United States of America, vol. 34, pp. 204–207, 1948.
  • W. Zhang and D. Han, “On the sixth power mean of the two-term exponential sums,” Journal of Number Theory, vol. 136, pp. 403–413, 2014.
  • T. M. Apostol, Introduction to Analytic Number Theory, Springer, New York, NY, USA, 1976. \endinput