@article{YUAN2023, 
author = {Renjie YUAN and Tingting WANG},
title = {On the fourth power mean value of one kind two-term exponential sums},
year = {2023},
journal = {Journal of Northwest University (Natural Science Edition)},
volume = {53},
number = {3},
pages = {453-458},
keywords = {the two-term exponential sums, fourth power mean, computational formula, analytic mathods},
url = {https://www.sciopen.com/article/10.16152/j.cnki.xdxbzr.2023-03-016},
doi = {10.16152/j.cnki.xdxbzr.2023-03-016},
abstract = {The calculation of the mean value of exponential sums C(m, n, r, s; q) and its upper bound estimation is closely related to many number theory problems, such as Waring’s problem. Let p be an odd prime, this paper focuses on the problem of the calculation of the fourth power mean value of one kind two-term exponential sums when parameter n=1 and exponent r=4,  s=2. By utilizing the analytic methods, the odd-even property and orthogonality of Dirichlet character, and the properties of the character sums, we study the calculating problem of the fourth power mean of the two-term exponential sums for the form as C(m, 1, 4, 2; p), and give an exact calculating formula for it when the prime p≡3 mod 4. At the same time, for such research content, some open problems in this field are also proposed.}
}