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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 510534, 4 pages
Research Article

New Mixed Exponential Sums and Their Application

1Department of Science, Hetao College, Bayannur 015000, China
2School of Mathematics, Northwest University, Xi'an, Shaanxi 710127, China

Received 6 May 2014; Accepted 23 May 2014; Published 19 June 2014

Academic Editor: Ashraf Zenkour

Copyright © 2014 Yu Zhan and Xiaoxue Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The main purpose of this paper is to introduce a new mixed exponential sums and then use the analytic methods and the properties of Gauss sums to study the computational problems of the mean value involving these sums and give an interesting computational formula and a sharp upper bound estimate for these mixed exponential sums. As an application, we give a new asymptotic formula for the fourth power mean of Dirichlet -functions with the weight of these mixed exponential sums.