Abstract and Applied Analysis

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

Yahui Yu and Wenpeng Zhang

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 2 October 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


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

Export citation


  • 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