Affiliation:
1. Research Center for Number Theory and Its Applications, Northwest University , Xi’an , China
Abstract
Abstract
The main purpose of this article is to study the calculating problem of the fourth power mean of the two-term exponential sums and provide an accurate calculating formula for utilizing analytical methods and character sums’ properties. In the meantime, a result of the fourth power mean of Gauss sums is improved.
Reference13 articles.
1. R. Duan and W. P. Zhang, On the fourth power mean of the generalized two-term exponential sums, Math. Rep. 22 (2020), 205–212.
2. X. X. Li and Z. F. Xu, The fourth power mean of the generalized two-term exponential sums and its upper and lower bound estimates, J. Inequal. Appl. 504 (2013), 1–8, DOI: https://doi.org/10.1186/1029-242X-2013-504.
3. Z. Wenpeng, Moments of generalized quadratic Gauss sums weighted by L-functions, J. Number Theory 92 (2002), no. 2, 304–314.
4. Z. Wenpeng and L. Huaning, On the general Gauss sums and their fourth power mean, Osaka J. Math. 42 (2005), no. 1, 189–199.
5. N. Bag and R. Barman, Higher order moments of generalized quadratic Gauss sums weighted by L-functions, Asian J. Math. 25 (2021), 413–430.