On the fourth power mean of one kind generalized two-term exponential sums

The research on exponential sums is very important in number theory and practical application. This paper mainly discusses the properties of generalized two-term exponential sums. By means of elementary method, analytical method and the number of solutions of congruence equation, this paper studies the calculation of the fourth power mean of a kind of generalized two-term exponential sums, and gives an exact calculation formula and asymptotic formula. At the same time, the research results of this paper also provide some new and effective ideas and methods for the calculation of high-th two-term exponential sums, which is innovative.